Calculation of Color Score

Setup

Load Packages

##Install Packages if Needed
if (!require("ggplot2")) install.packages("ggplot2")
if (!require("vegan")) install.packages("vegan")

Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.6-4

if (!require("FactoMineR")) install.packages("FactoMineR")

Loading required package: FactoMineR
Warning: package ‘FactoMineR’ was built under R version 4.3.2Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

if (!require("factoextra")) install.packages("factoextra")

Loading required package: factoextra
Warning: package ‘factoextra’ was built under R version 4.3.2Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

##Load Packages
library("ggplot2")
library("vegan")
library("FactoMineR")
library("factoextra")

Note: Run “Graphing Parameters” section from 01_ExperimentalSetup.R file

Load and Organize Data

##Load Data
Color<-read.csv("Data/Color.csv", header=TRUE)
SampData<-read.csv("Data/SampleData.csv", header=TRUE)

##Set factor variables
SampData$TimeP<-factor(SampData$TimeP, levels=c("W1", "W2", "M1", "M4", "M8", "M12"), ordered=TRUE)
SampData$Site<-factor(SampData$Site, levels=c("KL", "SS"), ordered=TRUE)
SampData$Genotype<-factor(SampData$Genotype, levels=c("AC8", "AC10", "AC12"), ordered=TRUE)
SampData$Treatment<-factor(SampData$Treatment, levels=c("Control", "Heat"), ordered=TRUE)
SampData$Treat<-factor(SampData$Treat, levels=c("C", "H"), ordered=TRUE)

##Add a Sample Set Variable
SampData$Set<-paste(SampData$TimeP, SampData$Site, SampData$Genotype, SampData$Treat, sep=".")

##Set rownames to ID
rownames(SampData)<-SampData$ID
rownames(Color)<-Color$ID

##Merge Color data with Sample Meta Data
Color<-merge(Color, SampData, all.x=TRUE, all.y=FALSE)

##Add an Analysis Set Variable
Color$AnSet<-"Initial"
Color$AnSet[which(Color$TimeP=="M4" | Color$TimeP== "M8")]<-"Seasonal"
Color$AnSet[which(Color$TimeP=="M12")]<-"Annual"

##Add Season Variable
Color$Season<-"Summer"
Color$Season[which(Color$TimeP=="M4")]<-"Winter"
Color$Season[which(Color$TimeP=="M8")]<-"Spring"

Calculate Color Score

Standardize Colors

Standardize RGB colors by dividing Coral color by color standards.

Color$Red.Norm.Coral <- Color$Red.Coral/Color$Red.Standard
Color$Green.Norm.Coral <- Color$Green.Coral/Color$Green.Standard
Color$Blue.Norm.Coral <- Color$Blue.Coral/Color$Blue.Standard

Full Dataset

Distance Matrix

#Create matrix of standardized colors
Color.mat <- as.matrix(cbind(Color$Red.Norm.Coral,Color$Green.Norm.Coral,Color$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color.mat) <- Color$ID

#Create a Distance Matrix for PCA
Color.dist <- vegdist(Color.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color.PCA <- princomp(Color.dist) 

#Initial plot
fviz_pca_ind(Color.PCA)

#Check Variance Explained by Components
summary(Color.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     5.9664425 2.8510353 0.68377950 0.518671302 0.258287242
Proportion of Variance 0.7965234 0.1818749 0.01046164 0.006019384 0.001492703
Cumulative Proportion  0.7965234 0.9783983 0.98885997 0.994879352 0.996372055
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.228132003 0.1886893257 0.1249288424 0.1048593795
Proportion of Variance 0.001164502 0.0007966403 0.0003492151 0.0002460267
Cumulative Proportion  0.997536557 0.9983331971 0.9986824122 0.9989284389
                            Comp.10      Comp.11    Comp.12      Comp.13
Standard deviation     0.0959732912 0.0812139080 0.06894540 6.356276e-02
Proportion of Variance 0.0002060954 0.0001475803 0.00010636 9.040097e-05
Cumulative Proportion  0.9991345344 0.9992821147 0.99938847 9.994789e-01
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     5.465842e-02 5.228608e-02 4.240155e-02 0.0405928745
Proportion of Variance 6.684698e-05 6.117018e-05 4.022825e-05 0.0000368695
Cumulative Proportion  9.995457e-01 9.996069e-01 9.996471e-01 0.9996839905
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     3.871546e-02 3.223079e-02 3.099237e-02 3.024187e-02
Proportion of Variance 3.353794e-05 2.324394e-05 2.149202e-05 2.046374e-05
Cumulative Proportion  9.997175e-01 9.997408e-01 9.997623e-01 9.997827e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     2.913776e-02 2.577596e-02 2.447327e-02 2.240785e-02
Proportion of Variance 1.899678e-05 1.486611e-05 1.340145e-05 1.123487e-05
Cumulative Proportion  9.998017e-01 9.998166e-01 9.998300e-01 9.998412e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     2.048258e-02 1.979708e-02 1.961223e-02 1.841620e-02
Proportion of Variance 9.387223e-06 8.769404e-06 8.606402e-06 7.588702e-06
Cumulative Proportion  9.998506e-01 9.998594e-01 9.998680e-01 9.998756e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     1.734007e-02 1.650586e-02 1.565251e-02 1.492162e-02
Proportion of Variance 6.727745e-06 6.095986e-06 5.481955e-06 4.981953e-06
Cumulative Proportion  9.998823e-01 9.998884e-01 9.998939e-01 9.998989e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     1.477980e-02 1.382765e-02 1.346911e-02 1.296273e-02
Proportion of Variance 4.887703e-06 4.278234e-06 4.059245e-06 3.759764e-06
Cumulative Proportion  9.999038e-01 9.999080e-01 9.999121e-01 9.999159e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     1.242438e-02 1.225104e-02 1.202659e-02 1.143600e-02
Proportion of Variance 3.453955e-06 3.358255e-06 3.236327e-06 2.926281e-06
Cumulative Proportion  9.999193e-01 9.999227e-01 9.999259e-01 9.999288e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     1.118674e-02 1.083474e-02 1.052343e-02 1.040281e-02
Proportion of Variance 2.800108e-06 2.626666e-06 2.477889e-06 2.421416e-06
Cumulative Proportion  9.999316e-01 9.999343e-01 9.999367e-01 9.999392e-01
                            Comp.46      Comp.47      Comp.48      Comp.49
Standard deviation     9.968095e-03 9.613069e-03 9.415915e-03 8.777450e-03
Proportion of Variance 2.223269e-06 2.067720e-06 1.983776e-06 1.723869e-06
Cumulative Proportion  9.999414e-01 9.999434e-01 9.999454e-01 9.999472e-01
                            Comp.50      Comp.51      Comp.52      Comp.53
Standard deviation     8.648309e-03 8.425567e-03 8.355585e-03 8.233017e-03
Proportion of Variance 1.673516e-06 1.588422e-06 1.562145e-06 1.516651e-06
Cumulative Proportion  9.999488e-01 9.999504e-01 9.999520e-01 9.999535e-01
                            Comp.54      Comp.55      Comp.56      Comp.57
Standard deviation     8.145378e-03 7.928311e-03 7.820005e-03 7.588224e-03
Proportion of Variance 1.484534e-06 1.406465e-06 1.368301e-06 1.288392e-06
Cumulative Proportion  9.999550e-01 9.999564e-01 9.999578e-01 9.999590e-01
                            Comp.58      Comp.59      Comp.60      Comp.61
Standard deviation     7.399217e-03 7.161826e-03 6.906023e-03 6.744576e-03
Proportion of Variance 1.225009e-06 1.147665e-06 1.067146e-06 1.017834e-06
Cumulative Proportion  9.999603e-01 9.999614e-01 9.999625e-01 9.999635e-01
                            Comp.62      Comp.63      Comp.64      Comp.65
Standard deviation     6.601241e-03 6.507639e-03 6.320673e-03 6.253688e-03
Proportion of Variance 9.750319e-07 9.475769e-07 8.939109e-07 8.750645e-07
Cumulative Proportion  9.999645e-01 9.999654e-01 9.999663e-01 9.999672e-01
                            Comp.66      Comp.67      Comp.68      Comp.69
Standard deviation     6.211587e-03 6.116272e-03 6.057045e-03 5.918658e-03
Proportion of Variance 8.633221e-07 8.370303e-07 8.208982e-07 7.838159e-07
Cumulative Proportion  9.999681e-01 9.999689e-01 9.999697e-01 9.999705e-01
                            Comp.70      Comp.71      Comp.72      Comp.73
Standard deviation     5.785461e-03 5.622312e-03 5.561254e-03 5.357277e-03
Proportion of Variance 7.489341e-07 7.072899e-07 6.920110e-07 6.421785e-07
Cumulative Proportion  9.999712e-01 9.999720e-01 9.999726e-01 9.999733e-01
                            Comp.74      Comp.75      Comp.76      Comp.77
Standard deviation     5.335074e-03 5.289929e-03 5.209589e-03 5.085456e-03
Proportion of Variance 6.368666e-07 6.261340e-07 6.072599e-07 5.786653e-07
Cumulative Proportion  9.999739e-01 9.999745e-01 9.999752e-01 9.999757e-01
                            Comp.78      Comp.79      Comp.80      Comp.81
Standard deviation     4.989684e-03 4.838376e-03 4.819534e-03 4.769787e-03
Proportion of Variance 5.570751e-07 5.238017e-07 5.197298e-07 5.090561e-07
Cumulative Proportion  9.999763e-01 9.999768e-01 9.999773e-01 9.999778e-01
                            Comp.82      Comp.83      Comp.84      Comp.85
Standard deviation     4.684600e-03 4.624466e-03 4.594120e-03 4.554965e-03
Proportion of Variance 4.910352e-07 4.785098e-07 4.722504e-07 4.642348e-07
Cumulative Proportion  9.999783e-01 9.999788e-01 9.999793e-01 9.999797e-01
                            Comp.86      Comp.87      Comp.88      Comp.89
Standard deviation     4.522164e-03 4.496939e-03 4.314698e-03 4.183138e-03
Proportion of Variance 4.575729e-07 4.524824e-07 4.165513e-07 3.915362e-07
Cumulative Proportion  9.999802e-01 9.999807e-01 9.999811e-01 9.999815e-01
                            Comp.90      Comp.91      Comp.92      Comp.93
Standard deviation     4.119743e-03 4.086918e-03 4.053485e-03 4.029879e-03
Proportion of Variance 3.797588e-07 3.737313e-07 3.676416e-07 3.633722e-07
Cumulative Proportion  9.999818e-01 9.999822e-01 9.999826e-01 9.999830e-01
                            Comp.94      Comp.95      Comp.96      Comp.97
Standard deviation     3.971662e-03 3.956274e-03 3.907113e-03 3.837975e-03
Proportion of Variance 3.529492e-07 3.502196e-07 3.415699e-07 3.295884e-07
Cumulative Proportion  9.999833e-01 9.999837e-01 9.999840e-01 9.999843e-01
                            Comp.98      Comp.99     Comp.100     Comp.101
Standard deviation     3.829425e-03 3.809326e-03 3.774525e-03 3.687694e-03
Proportion of Variance 3.281216e-07 3.246862e-07 3.187809e-07 3.042827e-07
Cumulative Proportion  9.999847e-01 9.999850e-01 9.999853e-01 9.999856e-01
                           Comp.102     Comp.103     Comp.104     Comp.105
Standard deviation     3.649271e-03 3.619276e-03 3.588033e-03 3.553751e-03
Proportion of Variance 2.979751e-07 2.930967e-07 2.880584e-07 2.825802e-07
Cumulative Proportion  9.999859e-01 9.999862e-01 9.999865e-01 9.999868e-01
                           Comp.106     Comp.107     Comp.108     Comp.109
Standard deviation     3.471837e-03 3.443214e-03 3.396169e-03 3.352219e-03
Proportion of Variance 2.697034e-07 2.652746e-07 2.580752e-07 2.514388e-07
Cumulative Proportion  9.999870e-01 9.999873e-01 9.999876e-01 9.999878e-01
                           Comp.110     Comp.111     Comp.112     Comp.113
Standard deviation     3.324612e-03 3.292361e-03 3.267038e-03 3.206243e-03
Proportion of Variance 2.473145e-07 2.425395e-07 2.388229e-07 2.300173e-07
Cumulative Proportion  9.999881e-01 9.999883e-01 9.999885e-01 9.999888e-01
                           Comp.114     Comp.115     Comp.116     Comp.117
Standard deviation     3.163716e-03 3.148919e-03 3.123593e-03 3.050255e-03
Proportion of Variance 2.239560e-07 2.218659e-07 2.183115e-07 2.081804e-07
Cumulative Proportion  9.999890e-01 9.999892e-01 9.999894e-01 9.999896e-01
                           Comp.118     Comp.119     Comp.120     Comp.121
Standard deviation     3.048168e-03 3.021563e-03 2.916867e-03 2.905232e-03
Proportion of Variance 2.078957e-07 2.042823e-07 1.903711e-07 1.888553e-07
Cumulative Proportion  9.999898e-01 9.999901e-01 9.999902e-01 9.999904e-01
                           Comp.122     Comp.123     Comp.124     Comp.125
Standard deviation     2.873967e-03 2.825439e-03 2.783979e-03 2.770090e-03
Proportion of Variance 1.848124e-07 1.786239e-07 1.734201e-07 1.716941e-07
Cumulative Proportion  9.999906e-01 9.999908e-01 9.999910e-01 9.999911e-01
                           Comp.126     Comp.127     Comp.128     Comp.129
Standard deviation     2.731920e-03 2.715562e-03 2.689263e-03 2.636361e-03
Proportion of Variance 1.669951e-07 1.650012e-07 1.618207e-07 1.555168e-07
Cumulative Proportion  9.999913e-01 9.999915e-01 9.999916e-01 9.999918e-01
                           Comp.130     Comp.131     Comp.132     Comp.133
Standard deviation     2.631937e-03 2.598599e-03 2.582565e-03 2.576490e-03
Proportion of Variance 1.549953e-07 1.510936e-07 1.492348e-07 1.485335e-07
Cumulative Proportion  9.999919e-01 9.999921e-01 9.999922e-01 9.999924e-01
                           Comp.134     Comp.135     Comp.136     Comp.137
Standard deviation     2.571974e-03 2.508692e-03 2.468875e-03 2.460109e-03
Proportion of Variance 1.480134e-07 1.408193e-07 1.363848e-07 1.354179e-07
Cumulative Proportion  9.999925e-01 9.999927e-01 9.999928e-01 9.999930e-01
                           Comp.138     Comp.139     Comp.140     Comp.141
Standard deviation     2.442051e-03 2.420842e-03 2.412396e-03 2.407093e-03
Proportion of Variance 1.334372e-07 1.311295e-07 1.302161e-07 1.296443e-07
Cumulative Proportion  9.999931e-01 9.999932e-01 9.999933e-01 9.999935e-01
                           Comp.142     Comp.143     Comp.144     Comp.145
Standard deviation     2.389039e-03 2.377346e-03 2.294145e-03 2.256746e-03
Proportion of Variance 1.277069e-07 1.264598e-07 1.177631e-07 1.139548e-07
Cumulative Proportion  9.999936e-01 9.999937e-01 9.999938e-01 9.999940e-01
                           Comp.146     Comp.147     Comp.148     Comp.149
Standard deviation     2.252202e-03 2.233323e-03 2.228537e-03 2.213427e-03
Proportion of Variance 1.134965e-07 1.116017e-07 1.111239e-07 1.096221e-07
Cumulative Proportion  9.999941e-01 9.999942e-01 9.999943e-01 9.999944e-01
                           Comp.150     Comp.151     Comp.152     Comp.153
Standard deviation     2.160566e-03 2.153091e-03 2.145484e-03 2.131114e-03
Proportion of Variance 1.044486e-07 1.037271e-07 1.029954e-07 1.016204e-07
Cumulative Proportion  9.999945e-01 9.999946e-01 9.999947e-01 9.999948e-01
                           Comp.154     Comp.155     Comp.156     Comp.157
Standard deviation     2.119014e-03 2.105134e-03 2.064156e-03 2.059234e-03
Proportion of Variance 1.004697e-07 9.915789e-08 9.533503e-08 9.488099e-08
Cumulative Proportion  9.999949e-01 9.999950e-01 9.999951e-01 9.999952e-01
                           Comp.158     Comp.159     Comp.160     Comp.161
Standard deviation     2.048058e-03 2.036807e-03 2.010423e-03 1.991899e-03
Proportion of Variance 9.385384e-08 9.282551e-08 9.043627e-08 8.877738e-08
Cumulative Proportion  9.999953e-01 9.999954e-01 9.999955e-01 9.999956e-01
                           Comp.162     Comp.163     Comp.164     Comp.165
Standard deviation     1.989235e-03 1.984660e-03 1.973171e-03 1.955564e-03
Proportion of Variance 8.854010e-08 8.813328e-08 8.711581e-08 8.556810e-08
Cumulative Proportion  9.999957e-01 9.999958e-01 9.999958e-01 9.999959e-01
                           Comp.166     Comp.167     Comp.168     Comp.169
Standard deviation     1.943474e-03 1.940369e-03 1.915096e-03 1.907583e-03
Proportion of Variance 8.451331e-08 8.424344e-08 8.206329e-08 8.142065e-08
Cumulative Proportion  9.999960e-01 9.999961e-01 9.999962e-01 9.999963e-01
                           Comp.170     Comp.171     Comp.172     Comp.173
Standard deviation     1.859351e-03 1.851943e-03 1.837288e-03 1.834061e-03
Proportion of Variance 7.735535e-08 7.674021e-08 7.553047e-08 7.526538e-08
Cumulative Proportion  9.999963e-01 9.999964e-01 9.999965e-01 9.999966e-01
                           Comp.174     Comp.175     Comp.176     Comp.177
Standard deviation     1.825247e-03 1.802683e-03 1.790922e-03 1.788947e-03
Proportion of Variance 7.454370e-08 7.271201e-08 7.176634e-08 7.160816e-08
Cumulative Proportion  9.999966e-01 9.999967e-01 9.999968e-01 9.999969e-01
                           Comp.178     Comp.179     Comp.180     Comp.181
Standard deviation     1.778801e-03 1.762585e-03 1.746689e-03 1.735029e-03
Proportion of Variance 7.079824e-08 6.951329e-08 6.826507e-08 6.735674e-08
Cumulative Proportion  9.999969e-01 9.999970e-01 9.999971e-01 9.999971e-01
                           Comp.182     Comp.183     Comp.184     Comp.185
Standard deviation     1.725138e-03 1.718401e-03 1.706134e-03 1.693086e-03
Proportion of Variance 6.659098e-08 6.607186e-08 6.513196e-08 6.413948e-08
Cumulative Proportion  9.999972e-01 9.999973e-01 9.999973e-01 9.999974e-01
                           Comp.186     Comp.187     Comp.188     Comp.189
Standard deviation     1.664172e-03 1.652802e-03 1.631724e-03 1.618344e-03
Proportion of Variance 6.196750e-08 6.112365e-08 5.957461e-08 5.860155e-08
Cumulative Proportion  9.999975e-01 9.999975e-01 9.999976e-01 9.999976e-01
                           Comp.190     Comp.191     Comp.192     Comp.193
Standard deviation     1.609639e-03 1.608006e-03 1.606843e-03 1.597612e-03
Proportion of Variance 5.797286e-08 5.785530e-08 5.777160e-08 5.710975e-08
Cumulative Proportion  9.999977e-01 9.999977e-01 9.999978e-01 9.999979e-01
                           Comp.194     Comp.195     Comp.196     Comp.197
Standard deviation     1.578069e-03 1.577663e-03 1.533486e-03 1.518076e-03
Proportion of Variance 5.572106e-08 5.569239e-08 5.261712e-08 5.156498e-08
Cumulative Proportion  9.999979e-01 9.999980e-01 9.999980e-01 9.999981e-01
                           Comp.198     Comp.199     Comp.200     Comp.201
Standard deviation     1.488652e-03 1.474405e-03 1.469552e-03 1.454134e-03
Proportion of Variance 4.958542e-08 4.864089e-08 4.832120e-08 4.731257e-08
Cumulative Proportion  9.999981e-01 9.999982e-01 9.999982e-01 9.999983e-01
                           Comp.202     Comp.203     Comp.204     Comp.205
Standard deviation     1.449120e-03 1.438415e-03 1.397804e-03 1.393404e-03
Proportion of Variance 4.698688e-08 4.629523e-08 4.371800e-08 4.344321e-08
Cumulative Proportion  9.999983e-01 9.999984e-01 9.999984e-01 9.999985e-01
                           Comp.206     Comp.207     Comp.208     Comp.209
Standard deviation     1.387434e-03 1.361689e-03 1.353110e-03 1.348979e-03
Proportion of Variance 4.307171e-08 4.148807e-08 4.096698e-08 4.071723e-08
Cumulative Proportion  9.999985e-01 9.999985e-01 9.999986e-01 9.999986e-01
                           Comp.210     Comp.211     Comp.212     Comp.213
Standard deviation     1.347279e-03 1.336348e-03 1.334581e-03 1.324888e-03
Proportion of Variance 4.061467e-08 3.995828e-08 3.985270e-08 3.927586e-08
Cumulative Proportion  9.999987e-01 9.999987e-01 9.999987e-01 9.999988e-01
                           Comp.214     Comp.215     Comp.216     Comp.217
Standard deviation     1.311872e-03 1.310251e-03 1.267522e-03 1.264293e-03
Proportion of Variance 3.850794e-08 3.841287e-08 3.594833e-08 3.576542e-08
Cumulative Proportion  9.999988e-01 9.999989e-01 9.999989e-01 9.999989e-01
                           Comp.218     Comp.219     Comp.220     Comp.221
Standard deviation     1.263446e-03 1.259024e-03 1.241592e-03 1.202814e-03
Proportion of Variance 3.571752e-08 3.546789e-08 3.449257e-08 3.237161e-08
Cumulative Proportion  9.999990e-01 9.999990e-01 9.999990e-01 9.999991e-01
                           Comp.222     Comp.223     Comp.224     Comp.225
Standard deviation     1.193523e-03 1.171591e-03 1.169104e-03 1.167437e-03
Proportion of Variance 3.187345e-08 3.071280e-08 3.058256e-08 3.049541e-08
Cumulative Proportion  9.999991e-01 9.999991e-01 9.999992e-01 9.999992e-01
                           Comp.226     Comp.227     Comp.228     Comp.229
Standard deviation     1.147310e-03 1.142949e-03 1.120022e-03 1.115528e-03
Proportion of Variance 2.945299e-08 2.922950e-08 2.806858e-08 2.784381e-08
Cumulative Proportion  9.999992e-01 9.999992e-01 9.999993e-01 9.999993e-01
                           Comp.230     Comp.231     Comp.232     Comp.233
Standard deviation     1.111854e-03 1.111304e-03 1.095567e-03 1.082954e-03
Proportion of Variance 2.766070e-08 2.763332e-08 2.685626e-08 2.624143e-08
Cumulative Proportion  9.999993e-01 9.999994e-01 9.999994e-01 9.999994e-01
                           Comp.234     Comp.235     Comp.236     Comp.237
Standard deviation     1.074515e-03 1.053603e-03 1.041945e-03 1.038050e-03
Proportion of Variance 2.583404e-08 2.483829e-08 2.429165e-08 2.411041e-08
Cumulative Proportion  9.999994e-01 9.999995e-01 9.999995e-01 9.999995e-01
                           Comp.238     Comp.239     Comp.240     Comp.241
Standard deviation     1.028661e-03 1.022137e-03 1.016758e-03 1.004640e-03
Proportion of Variance 2.367621e-08 2.337683e-08 2.313145e-08 2.258334e-08
Cumulative Proportion  9.999995e-01 9.999996e-01 9.999996e-01 9.999996e-01
                           Comp.242     Comp.243     Comp.244     Comp.245
Standard deviation     9.722268e-04 9.643719e-04 9.623448e-04 9.493652e-04
Proportion of Variance 2.114963e-08 2.080927e-08 2.072187e-08 2.016667e-08
Cumulative Proportion  9.999996e-01 9.999996e-01 9.999997e-01 9.999997e-01
                           Comp.246     Comp.247     Comp.248     Comp.249
Standard deviation     9.206713e-04 8.938307e-04 8.874138e-04 8.561169e-04
Proportion of Variance 1.896605e-08 1.787632e-08 1.762057e-08 1.639962e-08
Cumulative Proportion  9.999997e-01 9.999997e-01 9.999997e-01 9.999998e-01
                           Comp.250     Comp.251     Comp.252     Comp.253
Standard deviation     8.301200e-04 8.263898e-04 8.247686e-04 8.111069e-04
Proportion of Variance 1.541876e-08 1.528050e-08 1.522060e-08 1.472054e-08
Cumulative Proportion  9.999998e-01 9.999998e-01 9.999998e-01 9.999998e-01
                           Comp.254     Comp.255     Comp.256     Comp.257
Standard deviation     7.506775e-04 7.468775e-04 7.386947e-04 7.220588e-04
Proportion of Variance 1.260882e-08 1.248149e-08 1.220949e-08 1.166575e-08
Cumulative Proportion  9.999998e-01 9.999998e-01 9.999999e-01 9.999999e-01
                           Comp.258     Comp.259     Comp.260     Comp.261
Standard deviation     7.047350e-04 6.826576e-04 6.646714e-04 6.634525e-04
Proportion of Variance 1.111269e-08 1.042734e-08 9.885114e-09 9.848891e-09
Cumulative Proportion  9.999999e-01 9.999999e-01 9.999999e-01 9.999999e-01
                           Comp.262     Comp.263     Comp.264     Comp.265
Standard deviation     6.549162e-04 6.417443e-04 6.258298e-04 6.132098e-04
Proportion of Variance 9.597080e-09 9.214921e-09 8.763550e-09 8.413677e-09
Cumulative Proportion  9.999999e-01 9.999999e-01 9.999999e-01 9.999999e-01
                           Comp.266     Comp.267     Comp.268     Comp.269
Standard deviation     6.083387e-04 5.619286e-04 5.606398e-04 4.978484e-04
Proportion of Variance 8.280538e-09 7.065289e-09 7.032916e-09 5.545769e-09
Cumulative Proportion  1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
                           Comp.270     Comp.271     Comp.272     Comp.273
Standard deviation     4.834326e-04 4.691742e-04 4.667486e-04 3.909267e-04
Proportion of Variance 5.229251e-09 4.925335e-09 4.874541e-09 3.419465e-09
Cumulative Proportion  1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
                           Comp.274     Comp.275     Comp.276 Comp.277
Standard deviation     3.401131e-04 3.345836e-04 3.329745e-04        0
Proportion of Variance 2.588299e-09 2.504822e-09 2.480787e-09        0
Cumulative Proportion  1.000000e+00 1.000000e+00 1.000000e+00        1

#Visualize the importance of each principal component
fviz_eig(Color.PCA, addlabels = TRUE) 

PC1 Explains 79.7% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1<-sprintf("%1.2f",0.7965234*100)
PC1

[1] "79.65"

#% Variance PCA 2
PC2<-sprintf("%1.2f",0.1818749*100)
PC2

[1] "18.19"

#Prepare for Plotting
Color.PCA_scores <- as.data.frame(Color.PCA$scores[,c(1:2)])
Color.PCA_scores$ID<-rownames(Color.PCA_scores)
Color.PCA_scores<-merge(Color.PCA_scores, SampData)

#Plot PCA
Color.PCA.plot<-ggplot(data = Color.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1,"%)"), y=paste0('PC 2 (',PC2,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score (explains 79.7% of the variance in the color data). Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Extract Color Score

##Retain Metadata columns of interest
names(Color.PCA_scores)

 [1] "ID"        "Comp.1"    "Comp.2"    "RandN"     "TimeP"     "Site"     
 [7] "Genotype"  "Treat"     "Treatment" "Vol_ml"    "Wax.I_g"   "Wax.F_g"  
[13] "Set"      

ColorData<-Color.PCA_scores[,c(1,4:9,13)]

##Retain PC1 as Color Score
ColorData$Score_Full<-Color.PCA_scores$Comp.1

##Initial Visual Check
ggplot(ColorData, aes(x=Set, y=Score_Full)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Invert signs for Control > Heated
ColorData$Score_Full<-ColorData$Score_Full*(-1)

#Adding 20 to make all score values positive 
ColorData$Score_Full<- ColorData$Score_Full +20

##Initial Visual Check
ggplot(ColorData, aes(x=Set, y=Score_Full)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Plot by Treatment
ggplot(ColorData, aes(x=Treatment, y=Score_Full)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

By Timepoint

Repeat the calculation of Color Score for each Timepoint individually

W1

Distance Matrix

#Subset W1 Timepoint
Color_W1<-subset(Color, TimeP=="W1")

#Create matrix of standardized colors
Color_W1.mat <- as.matrix(cbind(Color_W1$Red.Norm.Coral,Color_W1$Green.Norm.Coral,Color_W1$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_W1.mat) <- Color_W1$ID

#Create a Distance Matrix for PCA
Color_W1.dist <- vegdist(Color_W1.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_W1.PCA <- princomp(Color_W1.dist) 

#Initial plot
fviz_pca_ind(Color_W1.PCA)

#Check Variance Explained by Components
summary(Color_W1.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     2.1086566 1.0032761 0.25961776 0.196208135 0.141338625
Proportion of Variance 0.7922463 0.1793451 0.01200929 0.006859343 0.003559346
Cumulative Proportion  0.7922463 0.9715914 0.98360067 0.990460018 0.994019365
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.102314050 0.0627331568 0.0608328509 0.0516031555
Proportion of Variance 0.001865173 0.0007012014 0.0006593634 0.0004744616
Cumulative Proportion  0.995884537 0.9965857387 0.9972451022 0.9977195637
                           Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.044076898 0.0431571169 0.0354515030 0.0347047544
Proportion of Variance 0.000346155 0.0003318588 0.0002239329 0.0002145984
Cumulative Proportion  0.998065719 0.9983975775 0.9986215104 0.9988361088
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0309601659 0.0279451927 0.0267165909 2.265396e-02
Proportion of Variance 0.0001707871 0.0001391434 0.0001271776 9.144013e-05
Cumulative Proportion  0.9990068959 0.9991460393 0.9992732169 9.993647e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     2.123310e-02 2.017703e-02 1.952956e-02 1.736587e-02
Proportion of Variance 8.032957e-05 7.253757e-05 6.795687e-05 5.373306e-05
Cumulative Proportion  9.994450e-01 9.995175e-01 9.995855e-01 9.996392e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.619615e-02 1.542738e-02 1.375474e-02 1.317188e-02
Proportion of Variance 4.673824e-05 4.240655e-05 3.370956e-05 3.091321e-05
Cumulative Proportion  9.996860e-01 9.997284e-01 9.997621e-01 9.997930e-01
                            Comp.26     Comp.27      Comp.28      Comp.29
Standard deviation     0.0128109337 0.011254397 1.088926e-02 0.0106737054
Proportion of Variance 0.0000292422 0.000022568 2.112736e-05 0.0000202992
Cumulative Proportion  0.9998222239 0.999844792 9.998659e-01 0.9998862184
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     9.942582e-03 0.0089965270 0.0084877761 0.0082860852
Proportion of Variance 1.761355e-05 0.0000144211 0.0000128362 0.0000122334
Cumulative Proportion  9.999038e-01 0.9999182531 0.9999310893 0.9999433227
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     7.755027e-03 7.357170e-03 6.973448e-03 6.840233e-03
Proportion of Variance 1.071557e-05 9.644288e-06 8.664502e-06 8.336627e-06
Cumulative Proportion  9.999540e-01 9.999637e-01 9.999723e-01 9.999807e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     6.656542e-03 6.264577e-03 3.991039e-03 2.988127e-03
Proportion of Variance 7.894887e-06 6.992492e-06 2.838052e-06 1.590914e-06
Cumulative Proportion  9.999886e-01 9.999956e-01 9.999984e-01 1.000000e+00
                       Comp.42
Standard deviation           0
Proportion of Variance       0
Cumulative Proportion        1

#Visualize the importance of each principal component
fviz_eig(Color_W1.PCA, addlabels = TRUE) 

PC1 Explains 79.2% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_W1<-sprintf("%1.2f",0.7922463*100)
PC1_W1

[1] "79.22"

#% Variance PCA 2
PC2_W1<-sprintf("%1.2f",0.1793451*100)
PC2_W1

[1] "17.93"

#Prepare for Plotting
Color_W1.PCA_scores <- as.data.frame(Color_W1.PCA$scores[,c(1:2)])
Color_W1.PCA_scores$ID<-rownames(Color_W1.PCA_scores)
Color_W1.PCA_scores<-merge(Color_W1.PCA_scores, SampData)

#Plot PCA
Color_W1.PCA.plot<-ggplot(data = Color_W1.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_W1.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_W1,"%)"), y=paste0('PC 2 (',PC2_W1,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_W1.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

W2

Distance Matrix

#Subset W2 Timepoint
Color_W2<-subset(Color, TimeP=="W2")

#Create matrix of standardized colors
Color_W2.mat <- as.matrix(cbind(Color_W2$Red.Norm.Coral,Color_W2$Green.Norm.Coral,Color_W2$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_W2.mat) <- Color_W2$ID

#Create a Distance Matrix for PCA
Color_W2.dist <- vegdist(Color_W2.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_W2.PCA <- princomp(Color_W2.dist) 

#Initial plot
fviz_pca_ind(Color_W2.PCA)

#Check Variance Explained by Components
summary(Color_W2.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     2.3552985 1.1413264 0.33060589 0.174140577 0.095153156
Proportion of Variance 0.7899334 0.1854891 0.01556395 0.004318158 0.001289273
Cumulative Proportion  0.7899334 0.9754225 0.99098642 0.995304582 0.996593855
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.086557371 0.0803894617 0.0462236633 0.0403168626
Proportion of Variance 0.001066858 0.0009202309 0.0003042477 0.0002314579
Cumulative Proportion  0.997660714 0.9985809445 0.9988851922 0.9991166501
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0376376806 2.632705e-02 2.496879e-02 2.086078e-02
Proportion of Variance 0.0002017178 9.869679e-05 8.877561e-05 6.196691e-05
Cumulative Proportion  0.9993183680 9.994171e-01 9.995058e-01 9.995678e-01
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     1.904118e-02 1.639261e-02 1.625494e-02 1.515508e-02
Proportion of Variance 5.162813e-05 3.826439e-05 3.762437e-05 3.270507e-05
Cumulative Proportion  9.996194e-01 9.996577e-01 9.996953e-01 9.997280e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     1.412499e-02 1.345800e-02 1.291583e-02 1.180588e-02
Proportion of Variance 2.841023e-05 2.579049e-05 2.375437e-05 1.984702e-05
Cumulative Proportion  9.997564e-01 9.997822e-01 9.998060e-01 9.998258e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.084875e-02 1.052100e-02 1.003868e-02 9.874342e-03
Proportion of Variance 1.675938e-05 1.576206e-05 1.434998e-05 1.388401e-05
Cumulative Proportion  9.998426e-01 9.998584e-01 9.998727e-01 9.998866e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     9.579537e-03 9.236945e-03 8.896153e-03 8.432389e-03
Proportion of Variance 1.306735e-05 1.214941e-05 1.126946e-05 1.012511e-05
Cumulative Proportion  9.998997e-01 9.999118e-01 9.999231e-01 9.999332e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     7.911581e-03 7.208763e-03 6.792079e-03 6.379183e-03
Proportion of Variance 8.913026e-06 7.399802e-06 6.569072e-06 5.794670e-06
Cumulative Proportion  9.999421e-01 9.999495e-01 9.999561e-01 9.999619e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     5.960964e-03 5.591949e-03 5.357038e-03 5.201265e-03
Proportion of Variance 5.059779e-06 4.452717e-06 4.086467e-06 3.852268e-06
Cumulative Proportion  9.999669e-01 9.999714e-01 9.999755e-01 9.999793e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     4.973003e-03 4.651363e-03 4.494040e-03 4.357619e-03
Proportion of Variance 3.521567e-06 3.080768e-06 2.875891e-06 2.703940e-06
Cumulative Proportion  9.999828e-01 9.999859e-01 9.999888e-01 9.999915e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     4.243583e-03 3.529546e-03 3.192298e-03 3.099115e-03
Proportion of Variance 2.564272e-06 1.773930e-06 1.451127e-06 1.367647e-06
Cumulative Proportion  9.999941e-01 9.999958e-01 9.999973e-01 9.999987e-01
                            Comp.46      Comp.47
Standard deviation     3.061869e-03 8.056914e-09
Proportion of Variance 1.334970e-06 9.243491e-18
Cumulative Proportion  1.000000e+00 1.000000e+00

#Visualize the importance of each principal component
fviz_eig(Color_W2.PCA, addlabels = TRUE) 

PC1 Explains 79% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_W2<-sprintf("%1.2f",0.7899334*100)
PC1_W2

[1] "78.99"

#% Variance PCA 2
PC2_W2<-sprintf("%1.2f",0.1854891*100)
PC2_W2

[1] "18.55"

#Prepare for Plotting
Color_W2.PCA_scores <- as.data.frame(Color_W2.PCA$scores[,c(1:2)])
Color_W2.PCA_scores$ID<-rownames(Color_W2.PCA_scores)
Color_W2.PCA_scores<-merge(Color_W2.PCA_scores, SampData)

#Plot PCA
Color_W2.PCA.plot<-ggplot(data = Color_W2.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_W2.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_W2,"%)"), y=paste0('PC 2 (',PC2_W2,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_W2.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

M1

Distance Matrix

#Subset M1 Timepoint
Color_M1<-subset(Color, TimeP=="M1")

#Create matrix of standardized colors
Color_M1.mat <- as.matrix(cbind(Color_M1$Red.Norm.Coral,Color_M1$Green.Norm.Coral,Color_M1$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_M1.mat) <- Color_M1$ID

#Create a Distance Matrix for PCA
Color_M1.dist <- vegdist(Color_M1.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_M1.PCA <- princomp(Color_M1.dist) 

#Initial plot
fviz_pca_ind(Color_M1.PCA)

#Check Variance Explained by Components
summary(Color_M1.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     2.0285708 0.7976034 0.22431251 0.163467489 0.075598397
Proportion of Variance 0.8482496 0.1311346 0.01037171 0.005508155 0.001178063
Cumulative Proportion  0.8482496 0.9793842 0.98975592 0.995264074 0.996442137
                             Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.0632784913 0.0583479718 0.0403731895 0.0388093762
Proportion of Variance 0.0008253831 0.0007017701 0.0003359924 0.0003104679
Cumulative Proportion  0.9972675197 0.9979692898 0.9983052822 0.9986157501
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0336945833 0.0307748838 0.0275274774 0.0237690746
Proportion of Variance 0.0002340257 0.0001952253 0.0001561982 0.0001164576
Cumulative Proportion  0.9988497758 0.9990450011 0.9992011993 0.9993176569
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0224549289 2.012014e-02 1.902218e-02 1.760162e-02
Proportion of Variance 0.0001039362 8.344593e-05 7.458713e-05 6.386291e-05
Cumulative Proportion  0.9994215931 9.995050e-01 9.995796e-01 9.996435e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     1.553573e-02 1.313256e-02 1.244459e-02 1.183515e-02
Proportion of Variance 4.975154e-05 3.555021e-05 3.192305e-05 2.887292e-05
Cumulative Proportion  9.996932e-01 9.997288e-01 9.997607e-01 9.997896e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.150007e-02 1.060741e-02 1.037989e-02 9.249358e-03
Proportion of Variance 2.726114e-05 2.319327e-05 2.220901e-05 1.763464e-05
Cumulative Proportion  9.998168e-01 9.998400e-01 9.998623e-01 9.998799e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     8.784558e-03 8.581892e-03 0.0080282734 7.080712e-03
Proportion of Variance 1.590681e-05 1.518132e-05 0.0000132858 1.033468e-05
Cumulative Proportion  9.998958e-01 9.999110e-01 0.9999242588 9.999346e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     6.761799e-03 6.355545e-03 6.007771e-03 5.938046e-03
Proportion of Variance 9.424705e-06 8.326239e-06 7.439952e-06 7.268260e-06
Cumulative Proportion  9.999440e-01 9.999523e-01 9.999598e-01 9.999671e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     5.588981e-03 5.372683e-03 4.937974e-03 4.789632e-03
Proportion of Variance 6.438855e-06 5.950121e-06 5.026213e-06 4.728764e-06
Cumulative Proportion  9.999735e-01 9.999794e-01 9.999845e-01 9.999892e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     4.348942e-03 3.069729e-03 2.821410e-03 2.693993e-03
Proportion of Variance 3.898616e-06 1.942421e-06 1.640876e-06 1.496016e-06
Cumulative Proportion  9.999931e-01 9.999950e-01 9.999967e-01 9.999982e-01
                            Comp.42      Comp.43 Comp.44
Standard deviation     2.279108e-03 1.913536e-03       0
Proportion of Variance 1.070713e-06 7.547733e-07       0
Cumulative Proportion  9.999992e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_M1.PCA, addlabels = TRUE) 

PC1 Explains 84.8% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_M1<-sprintf("%1.2f",0.8482496 *100)
PC1_M1

[1] "84.82"

#% Variance PCA 2
PC2_M1<-sprintf("%1.2f",0.1311346 *100)
PC2_M1

[1] "13.11"

#Prepare for Plotting
Color_M1.PCA_scores <- as.data.frame(Color_M1.PCA$scores[,c(1:2)])
Color_M1.PCA_scores$ID<-rownames(Color_M1.PCA_scores)
Color_M1.PCA_scores<-merge(Color_M1.PCA_scores, SampData)

#Plot PCA
Color_M1.PCA.plot<-ggplot(data = Color_M1.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_M1.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_M1,"%)"), y=paste0('PC 2 (',PC2_M1,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_M1.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

M4

Distance Matrix

#Subset M4 Timepoint
Color_M4<-subset(Color, TimeP=="M4")

#Create matrix of standardized colors
Color_M4.mat <- as.matrix(cbind(Color_M4$Red.Norm.Coral,Color_M4$Green.Norm.Coral,Color_M4$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_M4.mat) <- Color_M4$ID

#Create a Distance Matrix for PCA
Color_M4.dist <- vegdist(Color_M4.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_M4.PCA <- princomp(Color_M4.dist) 

#Initial plot
fviz_pca_ind(Color_M4.PCA)

#Check Variance Explained by Components
summary(Color_M4.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     1.2309346 0.7018463 0.15366039 0.120048435 0.093361902
Proportion of Variance 0.7338452 0.2385715 0.01143558 0.006979873 0.004221569
Cumulative Proportion  0.7338452 0.9724167 0.98385224 0.990832109 0.995053678
                            Comp.6      Comp.7       Comp.8       Comp.9
Standard deviation     0.053096900 0.038343465 0.0330487379 0.0287023366
Proportion of Variance 0.001365441 0.000712061 0.0005289861 0.0003989964
Cumulative Proportion  0.996419119 0.997131180 0.9976601659 0.9980591623
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0248875165 0.0238476306 0.0214482809 0.0184060325
Proportion of Variance 0.0002999837 0.0002754387 0.0002228022 0.0001640797
Cumulative Proportion  0.9983591460 0.9986345847 0.9988573869 0.9990214666
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0175464260 1.383209e-02 1.305697e-02 1.233098e-02
Proportion of Variance 0.0001491117 9.266378e-05 8.256949e-05 7.364273e-05
Cumulative Proportion  0.9991705783 9.992632e-01 9.993458e-01 9.994195e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     1.226782e-02 1.080529e-02 1.019493e-02 9.936816e-03
Proportion of Variance 7.289026e-05 5.654668e-05 5.033883e-05 4.782214e-05
Cumulative Proportion  9.994923e-01 9.995489e-01 9.995992e-01 9.996471e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     0.0088345025 8.167480e-03 7.928379e-03 7.367121e-03
Proportion of Variance 0.0000378006 3.230805e-05 3.044411e-05 2.628634e-05
Cumulative Proportion  0.9996848528 9.997172e-01 9.997476e-01 9.997739e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     7.331757e-03 6.472753e-03 6.268150e-03 6.116798e-03
Proportion of Variance 2.603458e-05 2.029143e-05 1.902888e-05 1.812102e-05
Cumulative Proportion  9.997999e-01 9.998202e-01 9.998392e-01 9.998574e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     5.943301e-03 5.841620e-03 5.272834e-03 5.248384e-03
Proportion of Variance 1.710763e-05 1.652727e-05 1.346551e-05 1.334092e-05
Cumulative Proportion  9.998745e-01 9.998910e-01 9.999045e-01 9.999178e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     4.566595e-03 4.468233e-03 4.438093e-03 4.176434e-03
Proportion of Variance 1.009995e-05 9.669546e-06 9.539537e-06 8.447840e-06
Cumulative Proportion  9.999279e-01 9.999376e-01 9.999471e-01 9.999556e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     3.945923e-03 3.913443e-03 3.737298e-03 3.495544e-03
Proportion of Variance 7.541048e-06 7.417413e-06 6.764723e-06 5.917851e-06
Cumulative Proportion  9.999631e-01 9.999705e-01 9.999773e-01 9.999832e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     3.278510e-03 3.203026e-03 2.732893e-03 1.845243e-03
Proportion of Variance 5.205802e-06 4.968844e-06 3.617262e-06 1.649080e-06
Cumulative Proportion  9.999884e-01 9.999934e-01 9.999970e-01 9.999986e-01
                            Comp.46      Comp.47 Comp.48
Standard deviation     1.461483e-03 8.103806e-04       0
Proportion of Variance 1.034480e-06 3.180626e-07       0
Cumulative Proportion  9.999997e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_M4.PCA, addlabels = TRUE) 

PC1 Explains 73.4% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_M4<-sprintf("%1.2f",0.7338452 *100)
PC1_M4

[1] "73.38"

#% Variance PCA 2
PC2_M4<-sprintf("%1.2f",0.2385715*100)
PC2_M4

[1] "23.86"

#Prepare for Plotting
Color_M4.PCA_scores <- as.data.frame(Color_M4.PCA$scores[,c(1:2)])
Color_M4.PCA_scores$ID<-rownames(Color_M4.PCA_scores)
Color_M4.PCA_scores<-merge(Color_M4.PCA_scores, SampData)

#Plot PCA
Color_M4.PCA.plot<-ggplot(data = Color_M4.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_M4.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_M4,"%)"), y=paste0('PC 2 (',PC2_M4,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_M4.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. *Note: These coordinates should not be multiplied by -1 for intuitive interpretation (Control > Heated), but will still be made positive by adding 20

M8

Distance Matrix

#Subset W1 Timepoint
Color_M8<-subset(Color, TimeP=="M8")

#Create matrix of standardized colors
Color_M8.mat <- as.matrix(cbind(Color_M8$Red.Norm.Coral,Color_M8$Green.Norm.Coral,Color_M8$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_M8.mat) <- Color_M8$ID

#Create a Distance Matrix for PCA
Color_M8.dist <- vegdist(Color_M8.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_M8.PCA <- princomp(Color_M8.dist) 

#Initial plot
fviz_pca_ind(Color_M8.PCA)

#Check Variance Explained by Components
summary(Color_M8.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3     Comp.4      Comp.5
Standard deviation     0.8098439 0.4333088 0.09461894 0.06515443 0.058919229
Proportion of Variance 0.7569193 0.2166915 0.01033245 0.00489931 0.004006463
Cumulative Proportion  0.7569193 0.9736108 0.98394326 0.98884257 0.992849031
                            Comp.6    Comp.7       Comp.8       Comp.9
Standard deviation     0.044077309 0.0308445 0.0246012130 0.0242826222
Proportion of Variance 0.002242214 0.0010980 0.0006984897 0.0006805157
Cumulative Proportion  0.995091245 0.9961892 0.9968877348 0.9975682505
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0184116841 0.0161493736 0.0142114594 0.0137494920
Proportion of Variance 0.0003912317 0.0003009944 0.0002330904 0.0002181827
Cumulative Proportion  0.9979594822 0.9982604765 0.9984935669 0.9987117496
                           Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.011334062 0.0109649690 0.0094676980 9.159072e-03
Proportion of Variance 0.000148258 0.0001387592 0.0001034513 9.681663e-05
Cumulative Proportion  0.998860008 0.9989987668 0.9991022181 9.991990e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     8.495106e-03 7.763228e-03 7.701411e-03 7.064981e-03
Proportion of Variance 8.328842e-05 6.955553e-05 6.845222e-05 5.760617e-05
Cumulative Proportion  9.992823e-01 9.993519e-01 9.994203e-01 9.994779e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     6.725859e-03 6.558260e-03 6.153358e-03 5.552261e-03
Proportion of Variance 5.220866e-05 4.963914e-05 4.369899e-05 3.557843e-05
Cumulative Proportion  9.995301e-01 9.995798e-01 9.996235e-01 9.996591e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     5.168112e-03 5.026726e-03 4.861890e-03 4.644134e-03
Proportion of Variance 3.082555e-05 2.916201e-05 2.728081e-05 2.489181e-05
Cumulative Proportion  9.996899e-01 9.997190e-01 9.997463e-01 9.997712e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     4.538340e-03 4.270442e-03 4.189387e-03 4.088007e-03
Proportion of Variance 2.377065e-05 2.104712e-05 2.025574e-05 1.928725e-05
Cumulative Proportion  9.997950e-01 9.998160e-01 9.998363e-01 9.998556e-01
                            Comp.34      Comp.35      Comp.36     Comp.37
Standard deviation     0.0039213027 3.808023e-03 3.674472e-03 0.003562953
Proportion of Variance 0.0000177463 1.673579e-05 1.558249e-05 0.000014651
Cumulative Proportion  0.9998733295 9.998901e-01 9.999056e-01 0.999920299
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     3.532163e-03 0.0033427124 3.257387e-03 3.131059e-03
Proportion of Variance 1.439887e-05 0.0000128957 1.224576e-05 1.131435e-05
Cumulative Proportion  9.999347e-01 0.9999475933 9.999598e-01 9.999712e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     2.405568e-03 2.325405e-03 2.170286e-03 1.993345e-03
Proportion of Variance 6.678552e-06 6.240856e-06 5.436017e-06 4.585768e-06
Cumulative Proportion  9.999778e-01 9.999841e-01 9.999895e-01 9.999941e-01
                            Comp.46      Comp.47 Comp.48
Standard deviation     1.900185e-03 1.227238e-03       0
Proportion of Variance 4.167147e-06 1.738219e-06       0
Cumulative Proportion  9.999983e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_M8.PCA, addlabels = TRUE) 

PC1 Explains 75.7% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_M8<-sprintf("%1.2f",0.7569193*100)
PC1_M8

[1] "75.69"

#% Variance PCA 2
PC2_M8<-sprintf("%1.2f",0.2166915 *100)
PC2_M8

[1] "21.67"

#Prepare for Plotting
Color_M8.PCA_scores <- as.data.frame(Color_M8.PCA$scores[,c(1:2)])
Color_M8.PCA_scores$ID<-rownames(Color_M8.PCA_scores)
Color_M8.PCA_scores<-merge(Color_M8.PCA_scores, SampData)

#Plot PCA
Color_M8.PCA.plot<-ggplot(data = Color_M8.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_M8.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_M8,"%)"), y=paste0('PC 2 (',PC2_M8,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_M8.PCA.plot

Samples align along PC1 according to Treatment, but less separation between Heated vs Control. Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

M12

Distance Matrix

#Subset M12 Timepoint
Color_M12<-subset(Color, TimeP=="M12")

#Create matrix of standardized colors
Color_M12.mat <- as.matrix(cbind(Color_M12$Red.Norm.Coral,Color_M12$Green.Norm.Coral,Color_M12$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_M12.mat) <- Color_M12$ID

#Create a Distance Matrix for PCA
Color_M12.dist <- vegdist(Color_M12.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_M12.PCA <- princomp(Color_M12.dist) 

#Initial plot
fviz_pca_ind(Color_M12.PCA)

#Check Variance Explained by Components
summary(Color_M12.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     2.6307486 1.2370753 0.35732936 0.255917262 0.155421527
Proportion of Variance 0.7953724 0.1758750 0.01467402 0.007526811 0.002776094
Cumulative Proportion  0.7953724 0.9712474 0.98592147 0.993448277 0.996224371
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.114260728 0.0884077564 0.0516402054 0.0451547781
Proportion of Variance 0.001500396 0.0008982404 0.0003064699 0.0002343254
Cumulative Proportion  0.997724767 0.9986230073 0.9989294772 0.9991638026
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0373756136 0.0318318636 2.670671e-02 2.540062e-02
Proportion of Variance 0.0001605419 0.0001164491 8.196959e-05 7.414817e-05
Cumulative Proportion  0.9993243445 0.9994407936 9.995228e-01 9.995969e-01
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0230883094 2.010675e-02 1.808484e-02 1.604439e-02
Proportion of Variance 0.0000612627 4.646176e-05 3.758732e-05 2.958408e-05
Cumulative Proportion  0.9996581740 9.997046e-01 9.997422e-01 9.997718e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     0.0153445439 1.400353e-02 1.316914e-02 1.261185e-02
Proportion of Variance 0.0000270595 2.253653e-05 1.993088e-05 1.827973e-05
Cumulative Proportion  0.9997988667 9.998214e-01 9.998413e-01 9.998596e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.175780e-02 1.124303e-02 1.049205e-02 1.016488e-02
Proportion of Variance 1.588781e-05 1.452709e-05 1.265121e-05 1.187453e-05
Cumulative Proportion  9.998755e-01 9.998900e-01 9.999027e-01 9.999146e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     9.578818e-03 8.615514e-03 7.597832e-03 7.375186e-03
Proportion of Variance 1.054474e-05 8.530494e-06 6.634240e-06 6.251120e-06
Cumulative Proportion  9.999251e-01 9.999336e-01 9.999403e-01 9.999465e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     6.717477e-03 6.686356e-03 6.352131e-03 6.341865e-03
Proportion of Variance 5.185902e-06 5.137961e-06 4.637146e-06 4.622169e-06
Cumulative Proportion  9.999517e-01 9.999568e-01 9.999615e-01 9.999661e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     6.170623e-03 5.678885e-03 5.446104e-03 5.427442e-03
Proportion of Variance 4.375925e-06 3.706278e-06 3.408660e-06 3.385340e-06
Cumulative Proportion  9.999705e-01 9.999742e-01 9.999776e-01 9.999810e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     5.148174e-03 5.099105e-03 5.070893e-03 4.710738e-03
Proportion of Variance 3.045919e-06 2.988132e-06 2.955158e-06 2.550291e-06
Cumulative Proportion  9.999840e-01 9.999870e-01 9.999900e-01 9.999925e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     4.403416e-03 3.870200e-03 3.571450e-03 3.159518e-03
Proportion of Variance 2.228390e-06 1.721388e-06 1.465888e-06 1.147238e-06
Cumulative Proportion  9.999947e-01 9.999965e-01 9.999979e-01 9.999991e-01
                            Comp.46      Comp.47 Comp.48
Standard deviation     2.376894e-03 1.543709e-03       0
Proportion of Variance 6.492793e-07 2.738689e-07       0
Cumulative Proportion  9.999997e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_M12.PCA, addlabels = TRUE) 

PC1 Explains 79.5% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_M12<-sprintf("%1.2f",0.7953724*100)
PC1_M12

[1] "79.54"

#% Variance PCA 2
PC2_M12<-sprintf("%1.2f",0.1758750*100)
PC2_M12

[1] "17.59"

#Prepare for Plotting
Color_M12.PCA_scores <- as.data.frame(Color_M12.PCA$scores[,c(1:2)])
Color_M12.PCA_scores$ID<-rownames(Color_M12.PCA_scores)
Color_M12.PCA_scores<-merge(Color_M12.PCA_scores, SampData)

#Plot PCA
Color_M12.PCA.plot<-ggplot(data = Color_M12.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_M12.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_M12,"%)"), y=paste0('PC 2 (',PC2_M12,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_M12.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Extract Color Scores

##Combine results from individual timepoints
ColorData.TP<-rbind(Color_W1.PCA_scores, Color_W2.PCA_scores, 
                    Color_M1.PCA_scores, Color_M4.PCA_scores,
                    Color_M8.PCA_scores, Color_M12.PCA_scores)

##Retain PC1 as Color Score
ColorData.TP$Score_TP<-ColorData.TP$Comp.1

##Invert signs for Control > Heated for all except M4
ColorData.TP$Score_TP[-c(which(ColorData.TP$TimeP=="M4"))]<-ColorData.TP$Score_TP[-c(which(ColorData.TP$TimeP=="M4"))]*(-1)

#Adding 20 to make all score values positive 
ColorData.TP$Score_TP<- ColorData.TP$Score_TP +20

##Initial Visual Check
ggplot(ColorData.TP, aes(x=Set, y=Score_TP)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Plot by Treatment
ggplot(ColorData.TP, aes(x=Treatment, y=Score_TP)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Merge with Color Data
names(ColorData.TP)

 [1] "ID"        "Comp.1"    "Comp.2"    "RandN"     "TimeP"     "Site"     
 [7] "Genotype"  "Treat"     "Treatment" "Vol_ml"    "Wax.I_g"   "Wax.F_g"  
[13] "Set"       "Score_TP" 

ColorData<-merge(ColorData, ColorData.TP[,c(1,14)])

By Analysis Set

Repeat the calculation of Color Score for each Analysis Set. Initial: W1, W2, and M1 all from Aug 2022. Seasonal: M4 and M8 from Dec 2022 and Mar 2023. Annual: M12 from Aug 2023.

Initial

Distance Matrix

#Subset Initial Set
Color_IN<-subset(Color, AnSet=="Initial")

#Create matrix of standardized colors
Color_IN.mat <- as.matrix(cbind(Color_IN$Red.Norm.Coral,Color_IN$Green.Norm.Coral,Color_IN$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_IN.mat) <- Color_IN$ID

#Create a Distance Matrix for PCA
Color_IN.dist <- vegdist(Color_IN.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_IN.PCA <- princomp(Color_IN.dist) 

#Initial plot
fviz_pca_ind(Color_IN.PCA)

#Check Variance Explained by Components
summary(Color_IN.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     4.1826962 2.1657737 0.48586686 0.359847527 0.272587334
Proportion of Variance 0.7700304 0.2064531 0.01039034 0.005699441 0.003270443
Cumulative Proportion  0.7700304 0.9764835 0.98687385 0.992573288 0.995843731
                            Comp.6       Comp.7      Comp.8       Comp.9
Standard deviation     0.159242241 0.1446820580 0.107672222 0.0798730940
Proportion of Variance 0.001116122 0.0009213499 0.000510273 0.0002807995
Cumulative Proportion  0.996959854 0.9978812035 0.998391477 0.9986722760
                            Comp.10      Comp.11     Comp.12      Comp.13
Standard deviation     0.0715241421 0.0639132176 0.059260655 4.604625e-02
Proportion of Variance 0.0002251648 0.0001797946 0.000154571 9.332196e-05
Cumulative Proportion  0.9988974408 0.9990772354 0.999231806 9.993251e-01
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     4.008741e-02 3.970686e-02 3.517360e-02 3.273128e-02
Proportion of Variance 7.073123e-05 6.939469e-05 5.445389e-05 4.715429e-05
Cumulative Proportion  9.993959e-01 9.994653e-01 9.995197e-01 9.995669e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     2.898735e-02 2.808120e-02 2.575963e-02 2.299958e-02
Proportion of Variance 3.698387e-05 3.470776e-05 2.920615e-05 2.328279e-05
Cumulative Proportion  9.996038e-01 9.996386e-01 9.996678e-01 9.996910e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     2.186291e-02 2.052701e-02 2.024329e-02 1.862487e-02
Proportion of Variance 2.103833e-05 1.854584e-05 1.803671e-05 1.526799e-05
Cumulative Proportion  9.997121e-01 9.997306e-01 9.997487e-01 9.997639e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     1.815918e-02 1.686596e-02 1.663200e-02 1.589272e-02
Proportion of Variance 1.451402e-05 1.252038e-05 1.217543e-05 1.111711e-05
Cumulative Proportion  9.997784e-01 9.997910e-01 9.998031e-01 9.998143e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     1.574270e-02 1.532020e-02 1.420221e-02 1.381501e-02
Proportion of Variance 1.090821e-05 1.033057e-05 8.877841e-06 8.400353e-06
Cumulative Proportion  9.998252e-01 9.998355e-01 9.998444e-01 9.998528e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     1.332151e-02 1.283564e-02 1.261680e-02 1.206079e-02
Proportion of Variance 7.810916e-06 7.251545e-06 7.006375e-06 6.402463e-06
Cumulative Proportion  9.998606e-01 9.998678e-01 9.998748e-01 9.998812e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     1.124497e-02 1.086078e-02 1.053526e-02 1.009382e-02
Proportion of Variance 5.565602e-06 5.191793e-06 4.885237e-06 4.484422e-06
Cumulative Proportion  9.998868e-01 9.998920e-01 9.998969e-01 9.999014e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     9.930423e-03 9.455409e-03 9.350470e-03 9.219234e-03
Proportion of Variance 4.340410e-06 3.935101e-06 3.848240e-06 3.740976e-06
Cumulative Proportion  9.999057e-01 9.999096e-01 9.999135e-01 9.999172e-01
                            Comp.46      Comp.47      Comp.48      Comp.49
Standard deviation     9.035607e-03 8.839414e-03 8.727809e-03 8.650300e-03
Proportion of Variance 3.593436e-06 3.439079e-06 3.352785e-06 3.293499e-06
Cumulative Proportion  9.999208e-01 9.999243e-01 9.999276e-01 9.999309e-01
                            Comp.50      Comp.51      Comp.52      Comp.53
Standard deviation     8.172662e-03 8.053628e-03 7.767203e-03 7.677681e-03
Proportion of Variance 2.939831e-06 2.854818e-06 2.655367e-06 2.594510e-06
Cumulative Proportion  9.999339e-01 9.999367e-01 9.999394e-01 9.999420e-01
                            Comp.54      Comp.55      Comp.56      Comp.57
Standard deviation     7.334958e-03 7.012964e-03 6.972150e-03 6.579010e-03
Proportion of Variance 2.368048e-06 2.164704e-06 2.139581e-06 1.905093e-06
Cumulative Proportion  9.999443e-01 9.999465e-01 9.999486e-01 9.999505e-01
                            Comp.58      Comp.59      Comp.60      Comp.61
Standard deviation     6.544438e-03 6.391438e-03 6.148349e-03 6.072563e-03
Proportion of Variance 1.885124e-06 1.798011e-06 1.663843e-06 1.623078e-06
Cumulative Proportion  9.999524e-01 9.999542e-01 9.999559e-01 9.999575e-01
                            Comp.62      Comp.63      Comp.64      Comp.65
Standard deviation     6.013432e-03 5.883451e-03 5.679406e-03 5.605064e-03
Proportion of Variance 1.591623e-06 1.523560e-06 1.419715e-06 1.382791e-06
Cumulative Proportion  9.999591e-01 9.999606e-01 9.999620e-01 9.999634e-01
                            Comp.66      Comp.67      Comp.68      Comp.69
Standard deviation     5.501061e-03 5.435311e-03 5.298509e-03 5.261887e-03
Proportion of Variance 1.331951e-06 1.300301e-06 1.235670e-06 1.218648e-06
Cumulative Proportion  9.999648e-01 9.999661e-01 9.999673e-01 9.999685e-01
                            Comp.70      Comp.71      Comp.72      Comp.73
Standard deviation     5.238756e-03 5.158565e-03 5.140607e-03 5.081688e-03
Proportion of Variance 1.207957e-06 1.171259e-06 1.163119e-06 1.136609e-06
Cumulative Proportion  9.999697e-01 9.999709e-01 9.999721e-01 9.999732e-01
                            Comp.74      Comp.75      Comp.76      Comp.77
Standard deviation     4.921165e-03 4.877300e-03 4.703063e-03 4.666744e-03
Proportion of Variance 1.065936e-06 1.047018e-06 9.735466e-07 9.585685e-07
Cumulative Proportion  9.999743e-01 9.999753e-01 9.999763e-01 9.999772e-01
                            Comp.78      Comp.79      Comp.80      Comp.81
Standard deviation     4.605739e-03 4.576412e-03 4.564210e-03 4.430193e-03
Proportion of Variance 9.336711e-07 9.218184e-07 9.169096e-07 8.638544e-07
Cumulative Proportion  9.999782e-01 9.999791e-01 9.999800e-01 9.999809e-01
                            Comp.82      Comp.83      Comp.84      Comp.85
Standard deviation     4.327573e-03 4.169650e-03 4.084059e-03 3.998648e-03
Proportion of Variance 8.242976e-07 7.652344e-07 7.341406e-07 7.037552e-07
Cumulative Proportion  9.999817e-01 9.999825e-01 9.999832e-01 9.999839e-01
                            Comp.86      Comp.87      Comp.88      Comp.89
Standard deviation     3.916605e-03 3.806960e-03 3.770586e-03 3.718579e-03
Proportion of Variance 6.751726e-07 6.378989e-07 6.257675e-07 6.086243e-07
Cumulative Proportion  9.999846e-01 9.999852e-01 9.999858e-01 9.999864e-01
                            Comp.90      Comp.91      Comp.92      Comp.93
Standard deviation     3.637183e-03 3.591003e-03 3.553504e-03 3.481705e-03
Proportion of Variance 5.822716e-07 5.675796e-07 5.557877e-07 5.335551e-07
Cumulative Proportion  9.999870e-01 9.999876e-01 9.999882e-01 9.999887e-01
                            Comp.94      Comp.95      Comp.96      Comp.97
Standard deviation     3.464752e-03 3.426086e-03 3.421553e-03 3.383552e-03
Proportion of Variance 5.283716e-07 5.166445e-07 5.152783e-07 5.038961e-07
Cumulative Proportion  9.999892e-01 9.999897e-01 9.999902e-01 9.999908e-01
                            Comp.98      Comp.99     Comp.100     Comp.101
Standard deviation     3.366876e-03 3.328492e-03 3.245798e-03 3.181874e-03
Proportion of Variance 4.989413e-07 4.876298e-07 4.637011e-07 4.456164e-07
Cumulative Proportion  9.999913e-01 9.999917e-01 9.999922e-01 9.999926e-01
                           Comp.102     Comp.103     Comp.104     Comp.105
Standard deviation     3.082356e-03 3.076179e-03 3.030577e-03 3.012694e-03
Proportion of Variance 4.181778e-07 4.165033e-07 4.042462e-07 3.994895e-07
Cumulative Proportion  9.999931e-01 9.999935e-01 9.999939e-01 9.999943e-01
                           Comp.106     Comp.107     Comp.108     Comp.109
Standard deviation     2.958537e-03 2.849973e-03 2.788687e-03 2.765204e-03
Proportion of Variance 3.852558e-07 3.575006e-07 3.422904e-07 3.365501e-07
Cumulative Proportion  9.999947e-01 9.999950e-01 9.999954e-01 9.999957e-01
                           Comp.110     Comp.111     Comp.112     Comp.113
Standard deviation     2.710038e-03 2.702422e-03 2.625591e-03 2.576072e-03
Proportion of Variance 3.232556e-07 3.214412e-07 3.034235e-07 2.920863e-07
Cumulative Proportion  9.999960e-01 9.999964e-01 9.999967e-01 9.999969e-01
                           Comp.114     Comp.115     Comp.116     Comp.117
Standard deviation     2.488275e-03 2.478443e-03 2.414752e-03 2.412794e-03
Proportion of Variance 2.725159e-07 2.703667e-07 2.566494e-07 2.562334e-07
Cumulative Proportion  9.999972e-01 9.999975e-01 9.999977e-01 9.999980e-01
                           Comp.118     Comp.119     Comp.120     Comp.121
Standard deviation     2.172755e-03 2.096889e-03 1.960744e-03 1.927494e-03
Proportion of Variance 2.077862e-07 1.935290e-07 1.692143e-07 1.635239e-07
Cumulative Proportion  9.999982e-01 9.999984e-01 9.999986e-01 9.999987e-01
                           Comp.122     Comp.123     Comp.124     Comp.125
Standard deviation     1.869706e-03 1.793586e-03 1.724265e-03 1.722076e-03
Proportion of Variance 1.538657e-07 1.415923e-07 1.308589e-07 1.305269e-07
Cumulative Proportion  9.999989e-01 9.999990e-01 9.999992e-01 9.999993e-01
                           Comp.126     Comp.127     Comp.128     Comp.129
Standard deviation     1.689744e-03 1.662524e-03 1.649268e-03 1.559736e-03
Proportion of Variance 1.256716e-07 1.216553e-07 1.197230e-07 1.070773e-07
Cumulative Proportion  9.999994e-01 9.999995e-01 9.999997e-01 9.999998e-01
                           Comp.130     Comp.131     Comp.132     Comp.133
Standard deviation     1.530742e-03 1.299190e-03 1.098459e-03 1.450001e-08
Proportion of Variance 1.031334e-07 7.429176e-08 5.310835e-08 9.254046e-18
Cumulative Proportion  9.999999e-01 9.999999e-01 1.000000e+00 1.000000e+00

#Visualize the importance of each principal component
fviz_eig(Color_IN.PCA, addlabels = TRUE) 

PC1 Explains 77% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_IN<-sprintf("%1.2f",0.7700304 *100)
PC1_IN

[1] "77.00"

#% Variance PCA 2
PC2_IN<-sprintf("%1.2f",0.2064531 *100)
PC2_IN

[1] "20.65"

#Prepare for Plotting
Color_IN.PCA_scores <- as.data.frame(Color_IN.PCA$scores[,c(1:2)])
Color_IN.PCA_scores$ID<-rownames(Color_IN.PCA_scores)
Color_IN.PCA_scores<-merge(Color_IN.PCA_scores, SampData)

#Plot PCA
Color_IN.PCA.plot<-ggplot(data = Color_IN.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_IN.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_IN,"%)"), y=paste0('PC 2 (',PC2_IN,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_IN.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Seasonal

Distance Matrix

#Subset Seasonal Set
Color_SE<-subset(Color, AnSet=="Seasonal")

#Create matrix of standardized colors
Color_SE.mat <- as.matrix(cbind(Color_SE$Red.Norm.Coral,Color_SE$Green.Norm.Coral,Color_SE$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_SE.mat) <- Color_SE$ID

#Create a Distance Matrix for PCA
Color_SE.dist <- vegdist(Color_SE.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_SE.PCA <- princomp(Color_SE.dist) 

#Initial plot
fviz_pca_ind(Color_SE.PCA)

#Check Variance Explained by Components
summary(Color_SE.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     1.7831269 1.0944132 0.23601658 0.158286727 0.109855292
Proportion of Variance 0.7083081 0.2668212 0.01240917 0.005581446 0.002688436
Cumulative Proportion  0.7083081 0.9751293 0.98753848 0.993119927 0.995808363
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.070421401 0.0595102457 0.0510308773 0.0378444968
Proportion of Variance 0.001104758 0.0007889349 0.0005801279 0.0003190533
Cumulative Proportion  0.996913121 0.9977020556 0.9982821836 0.9986012368
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0332508539 0.0273658172 0.0232401836 0.0219747848
Proportion of Variance 0.0002462994 0.0001668302 0.0001203197 0.0001075739
Cumulative Proportion  0.9988475362 0.9990143664 0.9991346861 0.9992422600
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     2.079529e-02 1.761341e-02 1.712233e-02 1.634345e-02
Proportion of Variance 9.633578e-05 6.911059e-05 6.531056e-05 5.950388e-05
Cumulative Proportion  9.993386e-01 9.994077e-01 9.994730e-01 9.995325e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     1.333195e-02 1.325816e-02 1.269150e-02 0.0112544501
Proportion of Variance 3.959544e-05 3.915835e-05 3.588256e-05 0.0000282167
Cumulative Proportion  9.995721e-01 9.996113e-01 9.996472e-01 0.9996753739
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.094100e-02 9.783721e-03 0.0090568507 8.625282e-03
Proportion of Variance 2.666684e-05 2.132386e-05 0.0000182731 1.657312e-05
Cumulative Proportion  9.997020e-01 9.997234e-01 0.9997416376 9.997582e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     8.158747e-03 7.940254e-03 7.697729e-03 7.481304e-03
Proportion of Variance 1.482875e-05 1.404515e-05 1.320028e-05 1.246845e-05
Cumulative Proportion  9.997730e-01 9.997871e-01 9.998003e-01 9.998128e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     7.157935e-03 7.053127e-03 6.784967e-03 6.448160e-03
Proportion of Variance 1.141388e-05 1.108207e-05 1.025541e-05 9.262524e-06
Cumulative Proportion  9.998242e-01 9.998352e-01 9.998455e-01 9.998548e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     6.148759e-03 5.901965e-03 5.509151e-03 5.296267e-03
Proportion of Variance 8.422338e-06 7.759808e-06 6.761250e-06 6.248811e-06
Cumulative Proportion  9.998632e-01 9.998709e-01 9.998777e-01 9.998840e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     5.191312e-03 5.068710e-03 4.909169e-03 4.794832e-03
Proportion of Variance 6.003603e-06 5.723379e-06 5.368755e-06 5.121587e-06
Cumulative Proportion  9.998900e-01 9.998957e-01 9.999011e-01 9.999062e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     4.724916e-03 4.589354e-03 4.534700e-03 4.480022e-03
Proportion of Variance 4.973315e-06 4.692031e-06 4.580943e-06 4.471137e-06
Cumulative Proportion  9.999112e-01 9.999158e-01 9.999204e-01 9.999249e-01
                            Comp.46      Comp.47      Comp.48      Comp.49
Standard deviation     4.284972e-03 4.018862e-03 3.792015e-03 3.764522e-03
Proportion of Variance 4.090286e-06 3.598023e-06 3.203301e-06 3.157020e-06
Cumulative Proportion  9.999290e-01 9.999326e-01 9.999358e-01 9.999389e-01
                            Comp.50      Comp.51      Comp.52      Comp.53
Standard deviation     3.715825e-03 3.637332e-03 3.554652e-03 3.460813e-03
Proportion of Variance 3.075872e-06 2.947295e-06 2.814828e-06 2.668173e-06
Cumulative Proportion  9.999420e-01 9.999450e-01 9.999478e-01 9.999504e-01
                            Comp.54      Comp.55      Comp.56      Comp.57
Standard deviation     3.347437e-03 3.220543e-03 3.190222e-03 3.171177e-03
Proportion of Variance 2.496217e-06 2.310553e-06 2.267251e-06 2.240261e-06
Cumulative Proportion  9.999529e-01 9.999553e-01 9.999575e-01 9.999598e-01
                            Comp.58      Comp.59      Comp.60      Comp.61
Standard deviation     3.141223e-03 3.087500e-03 3.017919e-03 2.948389e-03
Proportion of Variance 2.198140e-06 2.123595e-06 2.028956e-06 1.936544e-06
Cumulative Proportion  9.999620e-01 9.999641e-01 9.999661e-01 9.999681e-01
                            Comp.62      Comp.63      Comp.64      Comp.65
Standard deviation     2.917200e-03 2.843875e-03 2.770194e-03 2.707911e-03
Proportion of Variance 1.895790e-06 1.801685e-06 1.709535e-06 1.633528e-06
Cumulative Proportion  9.999699e-01 9.999717e-01 9.999735e-01 9.999751e-01
                            Comp.66      Comp.67      Comp.68      Comp.69
Standard deviation     2.679583e-03 2.619747e-03 2.598994e-03 2.559106e-03
Proportion of Variance 1.599529e-06 1.528890e-06 1.504764e-06 1.458930e-06
Cumulative Proportion  9.999767e-01 9.999782e-01 9.999797e-01 9.999812e-01
                            Comp.70      Comp.71      Comp.72      Comp.73
Standard deviation     2.499851e-03 2.470944e-03 2.465089e-03 2.448198e-03
Proportion of Variance 1.392150e-06 1.360139e-06 1.353701e-06 1.335213e-06
Cumulative Proportion  9.999826e-01 9.999839e-01 9.999853e-01 9.999866e-01
                            Comp.74      Comp.75      Comp.76      Comp.77
Standard deviation     2.360869e-03 2.321919e-03 2.212598e-03 2.182403e-03
Proportion of Variance 1.241656e-06 1.201024e-06 1.090593e-06 1.061030e-06
Cumulative Proportion  9.999879e-01 9.999891e-01 9.999902e-01 9.999912e-01
                            Comp.78      Comp.79      Comp.80      Comp.81
Standard deviation     2.091460e-03 2.043928e-03 1.953462e-03 1.929549e-03
Proportion of Variance 9.744440e-07 9.306552e-07 8.500954e-07 8.294097e-07
Cumulative Proportion  9.999922e-01 9.999931e-01 9.999940e-01 9.999948e-01
                            Comp.82      Comp.83      Comp.84      Comp.85
Standard deviation     1.844990e-03 1.778297e-03 1.673213e-03 1.537657e-03
Proportion of Variance 7.583084e-07 7.044760e-07 6.236773e-07 5.267163e-07
Cumulative Proportion  9.999956e-01 9.999963e-01 9.999969e-01 9.999974e-01
                            Comp.86      Comp.87      Comp.88      Comp.89
Standard deviation     1.483148e-03 1.374735e-03 1.340049e-03 1.152068e-03
Proportion of Variance 4.900345e-07 4.210132e-07 4.000363e-07 2.956743e-07
Cumulative Proportion  9.999979e-01 9.999983e-01 9.999987e-01 9.999990e-01
                            Comp.90      Comp.91      Comp.92      Comp.93
Standard deviation     1.074884e-03 9.947533e-04 9.217579e-04 8.529013e-04
Proportion of Variance 2.573837e-07 2.204390e-07 1.892742e-07 1.620523e-07
Cumulative Proportion  9.999993e-01 9.999995e-01 9.999997e-01 9.999999e-01
                            Comp.94      Comp.95      Comp.96
Standard deviation     5.806749e-04 5.703946e-04 8.811875e-09
Proportion of Variance 7.511451e-08 7.247838e-08 1.729794e-17
Cumulative Proportion  9.999999e-01 1.000000e+00 1.000000e+00

#Visualize the importance of each principal component
fviz_eig(Color_SE.PCA, addlabels = TRUE) 

PC1 Explains 70.8% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_SE<-sprintf("%1.2f",0.7083081  *100)
PC1_SE

[1] "70.83"

#% Variance PCA 2
PC2_SE<-sprintf("%1.2f",0.2668212  *100)
PC2_SE

[1] "26.68"

#Prepare for Plotting
Color_SE.PCA_scores <- as.data.frame(Color_SE.PCA$scores[,c(1:2)])
Color_SE.PCA_scores$ID<-rownames(Color_SE.PCA_scores)
Color_SE.PCA_scores<-merge(Color_SE.PCA_scores, SampData)

#Plot PCA
Color_SE.PCA.plot<-ggplot(data = Color_SE.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_SE.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_SE,"%)"), y=paste0('PC 2 (',PC2_SE,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_SE.PCA.plot

Samples align along PC1 according to Treatment, but less split between Heated vs Control. Coordinates along PC1 will be extracted as the Color Score. *Note: These coordinates should not be multiplied by -1 for intuitive interpretation (Control > Heated), but will still be made positive by adding 20

Annual

Distance Matrix

#Subset Annual Set
Color_AN<-subset(Color, AnSet=="Annual")

#Create matrix of standardized colors
Color_AN.mat <- as.matrix(cbind(Color_AN$Red.Norm.Coral,Color_AN$Green.Norm.Coral,Color_AN$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_AN.mat) <- Color_AN$ID

#Create a Distance Matrix for PCA
Color_AN.dist <- vegdist(Color_AN.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_AN.PCA <- princomp(Color_AN.dist) 

#Initial plot
fviz_pca_ind(Color_AN.PCA)

#Check Variance Explained by Components
summary(Color_AN.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     2.6307486 1.2370753 0.35732936 0.255917262 0.155421527
Proportion of Variance 0.7953724 0.1758750 0.01467402 0.007526811 0.002776094
Cumulative Proportion  0.7953724 0.9712474 0.98592147 0.993448277 0.996224371
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.114260728 0.0884077564 0.0516402054 0.0451547781
Proportion of Variance 0.001500396 0.0008982404 0.0003064699 0.0002343254
Cumulative Proportion  0.997724767 0.9986230073 0.9989294772 0.9991638026
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0373756136 0.0318318636 2.670671e-02 2.540062e-02
Proportion of Variance 0.0001605419 0.0001164491 8.196959e-05 7.414817e-05
Cumulative Proportion  0.9993243445 0.9994407936 9.995228e-01 9.995969e-01
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0230883094 2.010675e-02 1.808484e-02 1.604439e-02
Proportion of Variance 0.0000612627 4.646176e-05 3.758732e-05 2.958408e-05
Cumulative Proportion  0.9996581740 9.997046e-01 9.997422e-01 9.997718e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     0.0153445439 1.400353e-02 1.316914e-02 1.261185e-02
Proportion of Variance 0.0000270595 2.253653e-05 1.993088e-05 1.827973e-05
Cumulative Proportion  0.9997988667 9.998214e-01 9.998413e-01 9.998596e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     1.175780e-02 1.124303e-02 1.049205e-02 1.016488e-02
Proportion of Variance 1.588781e-05 1.452709e-05 1.265121e-05 1.187453e-05
Cumulative Proportion  9.998755e-01 9.998900e-01 9.999027e-01 9.999146e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     9.578818e-03 8.615514e-03 7.597832e-03 7.375186e-03
Proportion of Variance 1.054474e-05 8.530494e-06 6.634240e-06 6.251120e-06
Cumulative Proportion  9.999251e-01 9.999336e-01 9.999403e-01 9.999465e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     6.717477e-03 6.686356e-03 6.352131e-03 6.341865e-03
Proportion of Variance 5.185902e-06 5.137961e-06 4.637146e-06 4.622169e-06
Cumulative Proportion  9.999517e-01 9.999568e-01 9.999615e-01 9.999661e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     6.170623e-03 5.678885e-03 5.446104e-03 5.427442e-03
Proportion of Variance 4.375925e-06 3.706278e-06 3.408660e-06 3.385340e-06
Cumulative Proportion  9.999705e-01 9.999742e-01 9.999776e-01 9.999810e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     5.148174e-03 5.099105e-03 5.070893e-03 4.710738e-03
Proportion of Variance 3.045919e-06 2.988132e-06 2.955158e-06 2.550291e-06
Cumulative Proportion  9.999840e-01 9.999870e-01 9.999900e-01 9.999925e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     4.403416e-03 3.870200e-03 3.571450e-03 3.159518e-03
Proportion of Variance 2.228390e-06 1.721388e-06 1.465888e-06 1.147238e-06
Cumulative Proportion  9.999947e-01 9.999965e-01 9.999979e-01 9.999991e-01
                            Comp.46      Comp.47 Comp.48
Standard deviation     2.376894e-03 1.543709e-03       0
Proportion of Variance 6.492793e-07 2.738689e-07       0
Cumulative Proportion  9.999997e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_AN.PCA, addlabels = TRUE) 

PC1 Explains 79.5% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_AN<-sprintf("%1.2f",0.7953724  *100)
PC1_AN

[1] "79.54"

#% Variance PCA 2
PC2_AN<-sprintf("%1.2f",0.1758750  *100)
PC2_AN

[1] "17.59"

#Prepare for Plotting
Color_AN.PCA_scores <- as.data.frame(Color_AN.PCA$scores[,c(1:2)])
Color_AN.PCA_scores$ID<-rownames(Color_AN.PCA_scores)
Color_AN.PCA_scores<-merge(Color_AN.PCA_scores, SampData)

#Plot PCA
Color_AN.PCA.plot<-ggplot(data = Color_AN.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_AN.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_AN,"%)"), y=paste0('PC 2 (',PC2_AN,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_AN.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Extract Color Scores

##Combine results from individual timepoints
ColorData.Set<-rbind(Color_IN.PCA_scores, Color_SE.PCA_scores, 
                    Color_AN.PCA_scores)

##Retain PC1 as Color Score
ColorData.Set$Score_Set<-ColorData.Set$Comp.1

##Add an Analysis Set Variable
ColorData.Set$AnSet<-"Initial"
ColorData.Set$AnSet[which(ColorData.Set$TimeP=="M4" | ColorData.Set$TimeP== "M8")]<-"Seasonal"
ColorData.Set$AnSet[which(ColorData.Set$TimeP=="M12")]<-"Annual"

##Invert signs for Control > Heated for all except Seasonal
ColorData.Set$Score_Set[-c(which(ColorData.Set$AnSet=="Seasonal"))]<-ColorData.Set$Score_Set[-c(which(ColorData.Set$AnSet=="Seasonal"))]*(-1)

#Adding 20 to make all score values positive 
ColorData.Set$Score_Set<- ColorData.Set$Score_Set +20

##Initial Visual Check
ggplot(ColorData.Set, aes(x=Set, y=Score_Set)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Plot by Treatment
ggplot(ColorData.Set, aes(x=Treatment, y=Score_Set)) + 
  geom_boxplot(alpha=0.5, shape=2, outlier.shape = NA)+
  geom_jitter(shape=16, position=position_jitter(0.1))+
  theme(axis.text.x = element_text(angle = 90))

##Merge with Color Data
names(ColorData.Set)

 [1] "ID"        "Comp.1"    "Comp.2"    "RandN"     "TimeP"     "Site"     
 [7] "Genotype"  "Treat"     "Treatment" "Vol_ml"    "Wax.I_g"   "Wax.F_g"  
[13] "Set"       "Score_Set" "AnSet"    

ColorData<-merge(ColorData, ColorData.Set[,c(1,14)])

By Season

Repeat the calculation of Color Score for each Season. Summer: W1, W2, and M1 from Aug 2022 plus M12 from Aug 2023. Winter: M4 from Dec 2022. Spring: M8 from Mar 2023.

Summer

Distance Matrix

#Subset Summer Set
Color_SU<-subset(Color, Season=="Summer")

#Create matrix of standardized colors
Color_SU.mat <- as.matrix(cbind(Color_SU$Red.Norm.Coral,Color_SU$Green.Norm.Coral,Color_SU$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_SU.mat) <- Color_SU$ID

#Create a Distance Matrix for PCA
Color_SU.dist <- vegdist(Color_SU.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_SU.PCA <- princomp(Color_SU.dist) 

#Initial plot
fviz_pca_ind(Color_SU.PCA)

#Check Variance Explained by Components
summary(Color_SU.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3     Comp.4      Comp.5
Standard deviation     4.8915583 2.5331620 0.58144919 0.43952451 0.264126621
Proportion of Variance 0.7699187 0.2064792 0.01087862 0.00621608 0.002244785
Cumulative Proportion  0.7699187 0.9763979 0.98727651 0.99349259 0.995737379
                            Comp.6       Comp.7       Comp.8       Comp.9
Standard deviation     0.196631060 0.1709796771 0.1182729362 0.1015137033
Proportion of Variance 0.001244098 0.0009406745 0.0004501126 0.0003315887
Cumulative Proportion  0.996981477 0.9979221516 0.9983722642 0.9987038529
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0781748741 0.0763796129 0.0677732365 0.0570422849
Proportion of Variance 0.0001966458 0.0001877177 0.0001477974 0.0001046994
Cumulative Proportion  0.9989004987 0.9990882165 0.9992360139 0.9993407133
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     5.394553e-02 4.902570e-02 4.079330e-02 3.584349e-02
Proportion of Variance 9.363998e-05 7.733891e-05 5.354613e-05 4.134004e-05
Cumulative Proportion  9.994344e-01 9.995117e-01 9.995652e-01 9.996066e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     3.340871e-02 0.0301076889 2.933657e-02 2.711947e-02
Proportion of Variance 3.591451e-05 0.0000291679 2.769294e-05 2.366535e-05
Cumulative Proportion  9.996425e-01 0.9996716608 9.996994e-01 9.997230e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     2.566462e-02 2.417347e-02 2.269387e-02 2.101489e-02
Proportion of Variance 2.119435e-05 1.880305e-05 1.657171e-05 1.421034e-05
Cumulative Proportion  9.997442e-01 9.997630e-01 9.997796e-01 9.997938e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     0.0197659817 1.938922e-02 1.830301e-02 1.691773e-02
Proportion of Variance 0.0000125715 1.209682e-05 1.077942e-05 9.209474e-06
Cumulative Proportion  0.9998063700 9.998185e-01 9.998292e-01 9.998385e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     1.651537e-02 1.601172e-02 1.542648e-02 1.499796e-02
Proportion of Variance 8.776616e-06 8.249474e-06 7.657451e-06 7.237934e-06
Cumulative Proportion  9.998472e-01 9.998555e-01 9.998631e-01 9.998704e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     1.443250e-02 1.381923e-02 1.342281e-02 1.217527e-02
Proportion of Variance 6.702449e-06 6.144949e-06 5.797454e-06 4.769884e-06
Cumulative Proportion  9.998771e-01 9.998832e-01 9.998890e-01 9.998938e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     1.173751e-02 1.165155e-02 1.151573e-02 1.102541e-02
Proportion of Variance 4.433044e-06 4.368353e-06 4.267109e-06 3.911468e-06
Cumulative Proportion  9.998982e-01 9.999026e-01 9.999069e-01 9.999108e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     1.053519e-02 1.043742e-02 1.024650e-02 1.001860e-02
Proportion of Variance 3.571375e-06 3.505395e-06 3.378326e-06 3.229718e-06
Cumulative Proportion  9.999143e-01 9.999178e-01 9.999212e-01 9.999245e-01
                            Comp.46      Comp.47      Comp.48      Comp.49
Standard deviation     9.733882e-03 9.484444e-03 9.274579e-03 9.048981e-03
Proportion of Variance 3.048755e-06 2.894504e-06 2.767826e-06 2.634813e-06
Cumulative Proportion  9.999275e-01 9.999304e-01 9.999332e-01 9.999358e-01
                            Comp.50      Comp.51      Comp.52      Comp.53
Standard deviation     8.706959e-03 8.322465e-03 8.225174e-03 8.067931e-03
Proportion of Variance 2.439402e-06 2.228714e-06 2.176910e-06 2.094473e-06
Cumulative Proportion  9.999382e-01 9.999405e-01 9.999426e-01 9.999447e-01
                            Comp.54      Comp.55      Comp.56      Comp.57
Standard deviation     7.727035e-03 7.640141e-03 7.600167e-03 7.358393e-03
Proportion of Variance 1.921216e-06 1.878249e-06 1.858646e-06 1.742274e-06
Cumulative Proportion  9.999467e-01 9.999485e-01 9.999504e-01 9.999521e-01
                            Comp.58      Comp.59      Comp.60      Comp.61
Standard deviation     7.041795e-03 6.667268e-03 6.646761e-03 6.430422e-03
Proportion of Variance 1.595575e-06 1.430363e-06 1.421577e-06 1.330544e-06
Cumulative Proportion  9.999537e-01 9.999552e-01 9.999566e-01 9.999579e-01
                            Comp.62      Comp.63      Comp.64      Comp.65
Standard deviation     6.160445e-03 6.048996e-03 5.960336e-03 5.918472e-03
Proportion of Variance 1.221166e-06 1.177381e-06 1.143120e-06 1.127118e-06
Cumulative Proportion  9.999591e-01 9.999603e-01 9.999615e-01 9.999626e-01
                            Comp.66      Comp.67      Comp.68      Comp.69
Standard deviation     5.768823e-03 5.642129e-03 5.592999e-03 5.536619e-03
Proportion of Variance 1.070840e-06 1.024322e-06 1.006560e-06 9.863697e-07
Cumulative Proportion  9.999637e-01 9.999647e-01 9.999657e-01 9.999667e-01
                            Comp.70      Comp.71      Comp.72      Comp.73
Standard deviation     5.408631e-03 5.278131e-03 5.234859e-03 5.063060e-03
Proportion of Variance 9.412937e-07 8.964183e-07 8.817802e-07 8.248529e-07
Cumulative Proportion  9.999676e-01 9.999685e-01 9.999694e-01 9.999702e-01
                            Comp.74      Comp.75      Comp.76      Comp.77
Standard deviation     5.011592e-03 4.926231e-03 4.911640e-03 4.866279e-03
Proportion of Variance 8.081682e-07 7.808723e-07 7.762532e-07 7.619813e-07
Cumulative Proportion  9.999710e-01 9.999718e-01 9.999726e-01 9.999733e-01
                            Comp.78      Comp.79      Comp.80      Comp.81
Standard deviation     4.760604e-03 4.738263e-03 4.683397e-03 4.598794e-03
Proportion of Variance 7.292468e-07 7.224182e-07 7.057848e-07 6.805160e-07
Cumulative Proportion  9.999741e-01 9.999748e-01 9.999755e-01 9.999762e-01
                            Comp.82      Comp.83      Comp.84      Comp.85
Standard deviation     4.516136e-03 4.489048e-03 4.414349e-03 4.395698e-03
Proportion of Variance 6.562728e-07 6.484238e-07 6.270235e-07 6.217362e-07
Cumulative Proportion  9.999768e-01 9.999775e-01 9.999781e-01 9.999787e-01
                            Comp.86      Comp.87      Comp.88      Comp.89
Standard deviation     4.382661e-03 4.313718e-03 4.248274e-03 4.194347e-03
Proportion of Variance 6.180536e-07 5.987617e-07 5.807316e-07 5.660817e-07
Cumulative Proportion  9.999794e-01 9.999800e-01 9.999805e-01 9.999811e-01
                            Comp.90      Comp.91      Comp.92      Comp.93
Standard deviation     4.164089e-03 4.137535e-03 4.054804e-03 4.030350e-03
Proportion of Variance 5.579437e-07 5.508504e-07 5.290418e-07 5.226800e-07
Cumulative Proportion  9.999817e-01 9.999822e-01 9.999827e-01 9.999833e-01
                            Comp.94      Comp.95      Comp.96      Comp.97
Standard deviation     3.972372e-03 3.945312e-03 3.829803e-03 3.811305e-03
Proportion of Variance 5.077503e-07 5.008562e-07 4.719580e-07 4.674098e-07
Cumulative Proportion  9.999838e-01 9.999843e-01 9.999847e-01 9.999852e-01
                            Comp.98      Comp.99     Comp.100     Comp.101
Standard deviation     3.772533e-03 3.524232e-03 3.491178e-03 3.421693e-03
Proportion of Variance 4.579484e-07 3.996495e-07 3.921881e-07 3.767319e-07
Cumulative Proportion  9.999857e-01 9.999861e-01 9.999865e-01 9.999868e-01
                           Comp.102     Comp.103     Comp.104     Comp.105
Standard deviation     3.409835e-03 3.395956e-03 3.318040e-03 3.289384e-03
Proportion of Variance 3.741253e-07 3.710860e-07 3.542532e-07 3.481606e-07
Cumulative Proportion  9.999872e-01 9.999876e-01 9.999879e-01 9.999883e-01
                           Comp.106     Comp.107     Comp.108     Comp.109
Standard deviation     3.267900e-03 3.255476e-03 3.228306e-03 3.181721e-03
Proportion of Variance 3.436276e-07 3.410196e-07 3.353512e-07 3.257427e-07
Cumulative Proportion  9.999886e-01 9.999890e-01 9.999893e-01 9.999896e-01
                           Comp.110     Comp.111     Comp.112     Comp.113
Standard deviation     3.161413e-03 3.084246e-03 3.079741e-03 3.074371e-03
Proportion of Variance 3.215977e-07 3.060894e-07 3.051960e-07 3.041327e-07
Cumulative Proportion  9.999900e-01 9.999903e-01 9.999906e-01 9.999909e-01
                           Comp.114     Comp.115     Comp.116     Comp.117
Standard deviation     2.994603e-03 2.980454e-03 2.940033e-03 2.928299e-03
Proportion of Variance 2.885552e-07 2.858348e-07 2.781345e-07 2.759187e-07
Cumulative Proportion  9.999912e-01 9.999914e-01 9.999917e-01 9.999920e-01
                           Comp.118     Comp.119     Comp.120     Comp.121
Standard deviation     2.861354e-03 2.855350e-03 2.795740e-03 2.757646e-03
Proportion of Variance 2.634472e-07 2.623427e-07 2.515034e-07 2.446963e-07
Cumulative Proportion  9.999923e-01 9.999925e-01 9.999928e-01 9.999930e-01
                           Comp.122     Comp.123     Comp.124     Comp.125
Standard deviation     2.721554e-03 2.718007e-03 2.684701e-03 2.671416e-03
Proportion of Variance 2.383331e-07 2.377123e-07 2.319221e-07 2.296326e-07
Cumulative Proportion  9.999933e-01 9.999935e-01 9.999937e-01 9.999940e-01
                           Comp.126     Comp.127     Comp.128     Comp.129
Standard deviation     2.615013e-03 2.559642e-03 2.552890e-03 2.477776e-03
Proportion of Variance 2.200382e-07 2.108185e-07 2.097077e-07 1.975489e-07
Cumulative Proportion  9.999942e-01 9.999944e-01 9.999946e-01 9.999948e-01
                           Comp.130     Comp.131     Comp.132     Comp.133
Standard deviation     2.459162e-03 2.455953e-03 2.408848e-03 2.407398e-03
Proportion of Variance 1.945919e-07 1.940843e-07 1.867106e-07 1.864860e-07
Cumulative Proportion  9.999950e-01 9.999952e-01 9.999954e-01 9.999956e-01
                           Comp.134     Comp.135     Comp.136     Comp.137
Standard deviation     2.340052e-03 2.307746e-03 2.301377e-03 2.296209e-03
Proportion of Variance 1.761982e-07 1.713667e-07 1.704221e-07 1.696575e-07
Cumulative Proportion  9.999957e-01 9.999959e-01 9.999961e-01 9.999962e-01
                           Comp.138     Comp.139     Comp.140     Comp.141
Standard deviation     2.261618e-03 2.240437e-03 2.213104e-03 2.210734e-03
Proportion of Variance 1.645845e-07 1.615161e-07 1.575992e-07 1.572618e-07
Cumulative Proportion  9.999964e-01 9.999966e-01 9.999967e-01 9.999969e-01
                           Comp.142     Comp.143     Comp.144     Comp.145
Standard deviation     2.166795e-03 2.135584e-03 2.110592e-03 2.087620e-03
Proportion of Variance 1.510727e-07 1.467519e-07 1.433372e-07 1.402341e-07
Cumulative Proportion  9.999970e-01 9.999972e-01 9.999973e-01 9.999975e-01
                           Comp.146     Comp.147     Comp.148     Comp.149
Standard deviation     2.038759e-03 2.016575e-03 2.012446e-03 1.988920e-03
Proportion of Variance 1.337464e-07 1.308516e-07 1.303164e-07 1.272873e-07
Cumulative Proportion  9.999976e-01 9.999977e-01 9.999979e-01 9.999980e-01
                           Comp.150     Comp.151     Comp.152     Comp.153
Standard deviation     1.984969e-03 1.962661e-03 1.918415e-03 1.759514e-03
Proportion of Variance 1.267821e-07 1.239484e-07 1.184228e-07 9.961750e-08
Cumulative Proportion  9.999981e-01 9.999982e-01 9.999984e-01 9.999985e-01
                           Comp.154     Comp.155     Comp.156     Comp.157
Standard deviation     1.751617e-03 1.668932e-03 1.652206e-03 1.628488e-03
Proportion of Variance 9.872537e-08 8.962464e-08 8.783730e-08 8.533353e-08
Cumulative Proportion  9.999986e-01 9.999986e-01 9.999987e-01 9.999988e-01
                           Comp.158     Comp.159     Comp.160     Comp.161
Standard deviation     1.615044e-03 1.507085e-03 1.497130e-03 1.461142e-03
Proportion of Variance 8.393041e-08 7.308462e-08 7.212231e-08 6.869660e-08
Cumulative Proportion  9.999989e-01 9.999990e-01 9.999990e-01 9.999991e-01
                           Comp.162     Comp.163     Comp.164     Comp.165
Standard deviation     1.446359e-03 1.414114e-03 1.387981e-03 1.375334e-03
Proportion of Variance 6.731360e-08 6.434568e-08 6.198937e-08 6.086490e-08
Cumulative Proportion  9.999992e-01 9.999992e-01 9.999993e-01 9.999994e-01
                           Comp.166     Comp.167     Comp.168     Comp.169
Standard deviation     1.340003e-03 1.339709e-03 1.331433e-03 1.290526e-03
Proportion of Variance 5.777791e-08 5.775258e-08 5.704125e-08 5.358998e-08
Cumulative Proportion  9.999994e-01 9.999995e-01 9.999995e-01 9.999996e-01
                           Comp.170     Comp.171     Comp.172     Comp.173
Standard deviation     1.247973e-03 1.216443e-03 1.204189e-03 1.174165e-03
Proportion of Variance 5.011418e-08 4.761393e-08 4.665942e-08 4.436176e-08
Cumulative Proportion  9.999996e-01 9.999997e-01 9.999997e-01 9.999998e-01
                           Comp.174     Comp.175     Comp.176     Comp.177
Standard deviation     1.134842e-03 1.106004e-03 1.054603e-03 1.025443e-03
Proportion of Variance 4.144017e-08 3.936080e-08 3.578723e-08 3.383558e-08
Cumulative Proportion  9.999998e-01 9.999999e-01 9.999999e-01 9.999999e-01
                           Comp.178     Comp.179     Comp.180 Comp.181
Standard deviation     9.382422e-04 8.447040e-04 5.853120e-04        0
Proportion of Variance 2.832568e-08 2.295934e-08 1.102364e-08        0
Cumulative Proportion  1.000000e+00 1.000000e+00 1.000000e+00        1

#Visualize the importance of each principal component
fviz_eig(Color_SU.PCA, addlabels = TRUE) 

PC1 Explains 77% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_SU<-sprintf("%1.2f",0.7699187  *100)
PC1_SU

[1] "76.99"

#% Variance PCA 2
PC2_SU<-sprintf("%1.2f",0.2064792  *100)
PC2_SU

[1] "20.65"

#Prepare for Plotting
Color_SU.PCA_scores <- as.data.frame(Color_SU.PCA$scores[,c(1:2)])
Color_SU.PCA_scores$ID<-rownames(Color_SU.PCA_scores)
Color_SU.PCA_scores<-merge(Color_SU.PCA_scores, SampData)

#Plot PCA
Color_SU.PCA.plot<-ggplot(data = Color_SU.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_SU.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_SU,"%)"), y=paste0('PC 2 (',PC2_SU,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_SU.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Winter

Distance Matrix

#Subset Winter Set
Color_WI<-subset(Color, Season=="Winter")

#Create matrix of standardized colors
Color_WI.mat <- as.matrix(cbind(Color_WI$Red.Norm.Coral,Color_WI$Green.Norm.Coral,Color_WI$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_WI.mat) <- Color_WI$ID

#Create a Distance Matrix for PCA
Color_WI.dist <- vegdist(Color_WI.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_WI.PCA <- princomp(Color_WI.dist) 

#Initial plot
fviz_pca_ind(Color_WI.PCA)

#Check Variance Explained by Components
summary(Color_WI.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3      Comp.4      Comp.5
Standard deviation     1.2309346 0.7018463 0.15366039 0.120048435 0.093361902
Proportion of Variance 0.7338452 0.2385715 0.01143558 0.006979873 0.004221569
Cumulative Proportion  0.7338452 0.9724167 0.98385224 0.990832109 0.995053678
                            Comp.6      Comp.7       Comp.8       Comp.9
Standard deviation     0.053096900 0.038343465 0.0330487379 0.0287023366
Proportion of Variance 0.001365441 0.000712061 0.0005289861 0.0003989964
Cumulative Proportion  0.996419119 0.997131180 0.9976601659 0.9980591623
                            Comp.10      Comp.11      Comp.12      Comp.13
Standard deviation     0.0248875165 0.0238476306 0.0214482809 0.0184060325
Proportion of Variance 0.0002999837 0.0002754387 0.0002228022 0.0001640797
Cumulative Proportion  0.9983591460 0.9986345847 0.9988573869 0.9990214666
                            Comp.14      Comp.15      Comp.16      Comp.17
Standard deviation     0.0175464260 1.383209e-02 1.305697e-02 1.233098e-02
Proportion of Variance 0.0001491117 9.266378e-05 8.256949e-05 7.364273e-05
Cumulative Proportion  0.9991705783 9.992632e-01 9.993458e-01 9.994195e-01
                            Comp.18      Comp.19      Comp.20      Comp.21
Standard deviation     1.226782e-02 1.080529e-02 1.019493e-02 9.936816e-03
Proportion of Variance 7.289026e-05 5.654668e-05 5.033883e-05 4.782214e-05
Cumulative Proportion  9.994923e-01 9.995489e-01 9.995992e-01 9.996471e-01
                            Comp.22      Comp.23      Comp.24      Comp.25
Standard deviation     0.0088345025 8.167480e-03 7.928379e-03 7.367121e-03
Proportion of Variance 0.0000378006 3.230805e-05 3.044411e-05 2.628634e-05
Cumulative Proportion  0.9996848528 9.997172e-01 9.997476e-01 9.997739e-01
                            Comp.26      Comp.27      Comp.28      Comp.29
Standard deviation     7.331757e-03 6.472753e-03 6.268150e-03 6.116798e-03
Proportion of Variance 2.603458e-05 2.029143e-05 1.902888e-05 1.812102e-05
Cumulative Proportion  9.997999e-01 9.998202e-01 9.998392e-01 9.998574e-01
                            Comp.30      Comp.31      Comp.32      Comp.33
Standard deviation     5.943301e-03 5.841620e-03 5.272834e-03 5.248384e-03
Proportion of Variance 1.710763e-05 1.652727e-05 1.346551e-05 1.334092e-05
Cumulative Proportion  9.998745e-01 9.998910e-01 9.999045e-01 9.999178e-01
                            Comp.34      Comp.35      Comp.36      Comp.37
Standard deviation     4.566595e-03 4.468233e-03 4.438093e-03 4.176434e-03
Proportion of Variance 1.009995e-05 9.669546e-06 9.539537e-06 8.447840e-06
Cumulative Proportion  9.999279e-01 9.999376e-01 9.999471e-01 9.999556e-01
                            Comp.38      Comp.39      Comp.40      Comp.41
Standard deviation     3.945923e-03 3.913443e-03 3.737298e-03 3.495544e-03
Proportion of Variance 7.541048e-06 7.417413e-06 6.764723e-06 5.917851e-06
Cumulative Proportion  9.999631e-01 9.999705e-01 9.999773e-01 9.999832e-01
                            Comp.42      Comp.43      Comp.44      Comp.45
Standard deviation     3.278510e-03 3.203026e-03 2.732893e-03 1.845243e-03
Proportion of Variance 5.205802e-06 4.968844e-06 3.617262e-06 1.649080e-06
Cumulative Proportion  9.999884e-01 9.999934e-01 9.999970e-01 9.999986e-01
                            Comp.46      Comp.47 Comp.48
Standard deviation     1.461483e-03 8.103806e-04       0
Proportion of Variance 1.034480e-06 3.180626e-07       0
Cumulative Proportion  9.999997e-01 1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_WI.PCA, addlabels = TRUE) 

PC1 Explains 73.4% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_WI<-sprintf("%1.2f",0.7338452  *100)
PC1_WI

[1] "73.38"

#% Variance PCA 2
PC2_WI<-sprintf("%1.2f",0.2385715  *100)
PC2_WI

[1] "23.86"

#Prepare for Plotting
Color_WI.PCA_scores <- as.data.frame(Color_WI.PCA$scores[,c(1:2)])
Color_WI.PCA_scores$ID<-rownames(Color_WI.PCA_scores)
Color_WI.PCA_scores<-merge(Color_WI.PCA_scores, SampData)

#Plot PCA
Color_WI.PCA.plot<-ggplot(data = Color_WI.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_WI.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_WI,"%)"), y=paste0('PC 2 (',PC2_WI,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_WI.PCA.plot

Samples align along PC1 according to Treatment (Heated vs Control). Coordinates along PC1 will be extracted as the Color Score. *Note: These coordinates should not be multiplied by -1 for intuitive interpretation (Control > Heated), but will still be made positive by adding 20

Spring

Distance Matrix

#Subset Spring Set
Color_SP<-subset(Color, Season=="Spring")

#Create matrix of standardized colors
Color_SP.mat <- as.matrix(cbind(Color_SP$Red.Norm.Coral,Color_SP$Green.Norm.Coral,Color_SP$Blue.Norm.Coral))

#Set row names to sample ID
rownames(Color_SP.mat) <- Color_SP$ID

#Create a Distance Matrix for PCA
Color_SP.dist <- vegdist(Color_SP.mat, method="euclidean", na.rm=TRUE)

PCA

#Run Principal Components Analysis
Color_SP.PCA <- princomp(Color_SP.dist) 

#Initial plot
fviz_pca_ind(Color_SP.PCA)

#Check Variance Explained by Components
summary(Color_SP.PCA)

Importance of components:
                          Comp.1    Comp.2     Comp.3     Comp.4      Comp.5
Standard deviation     0.8098439 0.4333088 0.09461894 0.06515443 0.058919229
Proportion of Variance 0.7569193 0.2166915 0.01033245 0.00489931 0.004006463
Cumulative Proportion  0.7569193 0.9736108 0.98394326 0.98884257 0.992849031
                            Comp.6    Comp.7       Comp.8       Comp.9      Comp.10
Standard deviation     0.044077309 0.0308445 0.0246012130 0.0242826222 0.0184116841
Proportion of Variance 0.002242214 0.0010980 0.0006984897 0.0006805157 0.0003912317
Cumulative Proportion  0.995091245 0.9961892 0.9968877348 0.9975682505 0.9979594822
                            Comp.11      Comp.12      Comp.13     Comp.14
Standard deviation     0.0161493736 0.0142114594 0.0137494920 0.011334062
Proportion of Variance 0.0003009944 0.0002330904 0.0002181827 0.000148258
Cumulative Proportion  0.9982604765 0.9984935669 0.9987117496 0.998860008
                            Comp.15      Comp.16      Comp.17      Comp.18
Standard deviation     0.0109649690 0.0094676980 9.159072e-03 8.495106e-03
Proportion of Variance 0.0001387592 0.0001034513 9.681663e-05 8.328842e-05
Cumulative Proportion  0.9989987668 0.9991022181 9.991990e-01 9.992823e-01
                            Comp.19      Comp.20      Comp.21      Comp.22
Standard deviation     7.763228e-03 7.701411e-03 7.064981e-03 6.725859e-03
Proportion of Variance 6.955553e-05 6.845222e-05 5.760617e-05 5.220866e-05
Cumulative Proportion  9.993519e-01 9.994203e-01 9.994779e-01 9.995301e-01
                            Comp.23      Comp.24      Comp.25      Comp.26
Standard deviation     6.558260e-03 6.153358e-03 5.552261e-03 5.168112e-03
Proportion of Variance 4.963914e-05 4.369899e-05 3.557843e-05 3.082555e-05
Cumulative Proportion  9.995798e-01 9.996235e-01 9.996591e-01 9.996899e-01
                            Comp.27      Comp.28      Comp.29      Comp.30
Standard deviation     5.026726e-03 4.861890e-03 4.644134e-03 4.538340e-03
Proportion of Variance 2.916201e-05 2.728081e-05 2.489181e-05 2.377065e-05
Cumulative Proportion  9.997190e-01 9.997463e-01 9.997712e-01 9.997950e-01
                            Comp.31      Comp.32      Comp.33      Comp.34
Standard deviation     4.270442e-03 4.189387e-03 4.088007e-03 0.0039213027
Proportion of Variance 2.104712e-05 2.025574e-05 1.928725e-05 0.0000177463
Cumulative Proportion  9.998160e-01 9.998363e-01 9.998556e-01 0.9998733295
                            Comp.35      Comp.36     Comp.37      Comp.38
Standard deviation     3.808023e-03 3.674472e-03 0.003562953 3.532163e-03
Proportion of Variance 1.673579e-05 1.558249e-05 0.000014651 1.439887e-05
Cumulative Proportion  9.998901e-01 9.999056e-01 0.999920299 9.999347e-01
                            Comp.39      Comp.40      Comp.41      Comp.42
Standard deviation     0.0033427124 3.257387e-03 3.131059e-03 2.405568e-03
Proportion of Variance 0.0000128957 1.224576e-05 1.131435e-05 6.678552e-06
Cumulative Proportion  0.9999475933 9.999598e-01 9.999712e-01 9.999778e-01
                            Comp.43      Comp.44      Comp.45      Comp.46
Standard deviation     2.325405e-03 2.170286e-03 1.993345e-03 1.900185e-03
Proportion of Variance 6.240856e-06 5.436017e-06 4.585768e-06 4.167147e-06
Cumulative Proportion  9.999841e-01 9.999895e-01 9.999941e-01 9.999983e-01
                            Comp.47 Comp.48
Standard deviation     1.227238e-03       0
Proportion of Variance 1.738219e-06       0
Cumulative Proportion  1.000000e+00       1

#Visualize the importance of each principal component
fviz_eig(Color_SP.PCA, addlabels = TRUE) 

PC1 Explains 75.7% of the variance in the color data.

Plot PCA

#% Variance PCA 1
PC1_SP<-sprintf("%1.2f",0.7569193  *100)
PC1_SP

[1] "75.69"

#% Variance PCA 2
PC2_SP<-sprintf("%1.2f",0.2166915  *100)
PC2_SP

[1] "21.67"

#Prepare for Plotting
Color_SP.PCA_scores <- as.data.frame(Color_SP.PCA$scores[,c(1:2)])
Color_SP.PCA_scores$ID<-rownames(Color_SP.PCA_scores)
Color_SP.PCA_scores<-merge(Color_SP.PCA_scores, SampData)

#Plot PCA
Color_SP.PCA.plot<-ggplot(data = Color_SP.PCA_scores, aes(x = Comp.1, y = Comp.2)) + 
  geom_point(data = Color_SP.PCA_scores, aes(colour = Treatment), size = point.sz-1, alpha = 0.8) + 
  scale_colour_manual(values =HC.colors.o)+
  theme_classic()+
  scale_x_continuous(limits = c(-6, 12))+
  scale_y_continuous(limits = c(-9, 9))+
  labs(x=paste0('PC 1 (',PC1_SP,"%)"), y=paste0('PC 2 (',PC2_SP,"%)"))+
   theme(axis.title.x = element_text(size = axis.title.sz), 
        axis.title.y = element_text(size = axis.title.sz), 
        axis.text.x=element_text(size=axis.txt.sz, colour="black"),
        axis.text.y=element_text(size=axis.txt.sz, colour="black"),
        legend.text=element_text(size=leg.txt.sz),
        legend.title=element_text(size=leg.title.sz),
        legend.box.background = element_rect(color = "black"), 
        legend.position="top");Color_SP.PCA.plot

Samples align along PC1 according to Treatment, but less separation between Heated vs Control. Coordinates along PC1 will be extracted as the Color Score. Coordinates will multiplied by -1 for intuitive interpretation (Control > Heated) then made positive by adding 20

Extract Color Scores

##Merge with Color Data
names(ColorData.Seas)

 [1] "ID"         "Comp.1"     "Comp.2"     "RandN"      "TimeP"      "Site"      
 [7] "Genotype"   "Treat"      "Treatment"  "Vol_ml"     "Wax.I_g"    "Wax.F_g"   
[13] "Set"        "Score_Seas" "Season"    

Compare Calculation Sets

Correlation

names(ColorData)

 [1] "ID"         "RandN"      "TimeP"      "Site"       "Genotype"   "Treat"     
 [7] "Treatment"  "Set"        "Score_Full" "Score_TP"   "Score_Set"  "Score_Seas"

cor(ColorData[,c(9:12)])

           Score_Full  Score_TP Score_Set Score_Seas
Score_Full  1.0000000 0.8008984 0.8934140  0.8943347
Score_TP    0.8008984 1.0000000 0.8524334  0.8858928
Score_Set   0.8934140 0.8524334 1.0000000  0.9583848
Score_Seas  0.8943347 0.8858928 0.9583848  1.0000000

chart.Correlation(ColorData[,c(9:12)], histogram=TRUE, pch=19)

All calculations of Color score between the Full Dataset, Individual PCA’s by Timepoints, or either Analysis / Seasonal sets are all highly correlated with each other.

Write Out Color Score Data

##Add an Analysis Set Variable
ColorData$AnSet<-"Initial"
ColorData$AnSet[which(ColorData$TimeP=="M4" | ColorData$TimeP== "M8")]<-"Seasonal"
ColorData$AnSet[which(ColorData$TimeP=="M12")]<-"Annual"

##Add Season Variable
ColorData$Season<-"Summer"
ColorData$Season[which(ColorData$TimeP=="M4")]<-"Winter"
ColorData$Season[which(ColorData$TimeP=="M8")]<-"Spring"

##Write out
write.csv(ColorData, "Outputs/ColorData.csv", row.names=FALSE)